Journal of Function Spaces The latest articles from Hindawi © 2017 , Hindawi Limited . All rights reserved. Existence and Multiplicity of Nontrivial Solutions for a Class of Semilinear Fractional Schrödinger Equations Tue, 26 Sep 2017 08:00:28 +0000 This paper is concerned with the existence of solutions to the following fractional Schrödinger type equations: , where the primitive of the nonlinearity is of superquadratic growth near infinity in and the potential is allowed to be sign-changing. By using variant Fountain theorems, a sufficient condition is obtained for the existence of infinitely many nontrivial high energy solutions. Xinsheng Du and Anmin Mao Copyright © 2017 Xinsheng Du and Anmin Mao. All rights reserved. Morrey Meets Herz with Variable Exponent and Applications to Commutators of Homogeneous Fractional Integrals with Rough Kernels Mon, 25 Sep 2017 00:00:00 +0000 We define the new central Morrey space with variable exponent and investigate its relation to the Morrey-Herz spaces with variable exponent. As applications, we obtain the boundedness of the homogeneous fractional integral operator and its commutator on Morrey-Herz space with variable exponent, where for is a homogeneous function of degree zero, , and is a BMO function. Hongbin Wang, Jiajia Wang, and Zunwei Fu Copyright © 2017 Hongbin Wang et al. All rights reserved. Existence of Mild Solutions and Controllability of Fractional Impulsive Integrodifferential Systems with Nonlocal Conditions Wed, 20 Sep 2017 00:00:00 +0000 This paper is concerned with the existence results of nonlocal problems for a class of fractional impulsive integrodifferential equations in Banach spaces. We define a piecewise continuous control function to obtain the results on controllability of the corresponding fractional impulsive integrodifferential control systems. The results are obtained by means of fixed point methods. An example to illustrate the applications of our main results is given. Haiyong Qin, Zhenyun Gu, Youliang Fu, and Tongxing Li Copyright © 2017 Haiyong Qin et al. All rights reserved. Restriction of Toeplitz Operators on Their Reducing Subspaces Thu, 07 Sep 2017 10:08:51 +0000 We study the restrictions of analytic Toeplitz operator on its minimal reducing subspaces for the unit disc and construct their models on slit domains. Furthermore, it is shown that is similar to the sum of copies of the Bergman shift. Anjian Xu and Yang Zou Copyright © 2017 Anjian Xu and Yang Zou. All rights reserved. On Fekete-Szegö Problems for Certain Subclasses Defined by -Derivative Thu, 07 Sep 2017 07:17:08 +0000 We derive the Fekete-Szegö theorem for new subclasses of analytic functions which are -analogue of well-known classes introduced before. Huda Aldweby and Maslina Darus Copyright © 2017 Huda Aldweby and Maslina Darus. All rights reserved. Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels Thu, 31 Aug 2017 00:00:00 +0000 We develop a generalized Jacobi-Galerkin method for second kind Volterra integral equations with weakly singular kernels. In this method, we first introduce some known singular nonpolynomial functions in the approximation space of the conventional Jacobi-Galerkin method. Secondly, we use the Gauss-Jacobi quadrature rules to approximate the integral term in the resulting equation so as to obtain high-order accuracy for the approximation. Then, we establish that the approximate equation has a unique solution and the approximate solution arrives at an optimal convergence order. One numerical example is presented to demonstrate the effectiveness of the proposed method. Haotao Cai Copyright © 2017 Haotao Cai. All rights reserved. Oscillation Criteria for Nonlinear Third-Order Neutral Dynamic Equations with Damping on Time Scales Mon, 28 Aug 2017 07:53:33 +0000 We establish several oscillation criteria for a class of third-order nonlinear dynamic equations with a damping term and a nonpositive neutral coefficient by using the Riccati transformation. Two illustrative examples are presented to show the significance of the results obtained. Yang-Cong Qiu, Akbar Zada, Haiyong Qin, and Tongxing Li Copyright © 2017 Yang-Cong Qiu et al. All rights reserved. Rogue Wave Solutions and Generalized Darboux Transformation for an Inhomogeneous Fifth-Order Nonlinear Schrödinger Equation Sun, 27 Aug 2017 08:22:55 +0000 The rogue wave solutions are discussed for an inhomogeneous fifth-order nonlinear Schrödinger equation, which describes the dynamics of a site-dependent Heisenberg ferromagnetic spin chain. Using the Darboux matrix, the generalized Darboux transformation is constructed and a recursive formula is derived. Based on the transformation, the first-order to the third-order rogue wave solutions are obtained. Then, the nonlinear dynamics of the first-order to the third-order rogue waves are studied on the basis of some free parameters. Several new structures of the rogue waves are found using numerical simulation. The conclusions will be a supportive tool to study the rogue waves better. N. Song, W. Zhang, P. Wang, and Y. K. Xue Copyright © 2017 N. Song et al. All rights reserved. A Regularity Criterion for the 3D Incompressible Magnetohydrodynamics Equations in the Multiplier Spaces Sun, 27 Aug 2017 07:50:19 +0000 We are concerned with the regularity criterion for weak solutions to the 3D incompressible MHD equations in this paper. We show that if some partial derivatives of the velocity components and magnetic components belong to the multiplier spaces, then the solution actually is smooth on . Chunhong Tian Copyright © 2017 Chunhong Tian. All rights reserved. Operator Inequalities of Morrey Spaces Associated with Karamata Regular Variation Thu, 24 Aug 2017 08:45:21 +0000 Karamata regular variation is a basic tool in stochastic process and the boundary blow-up problems for partial differential equations (PDEs). Morrey space is closely related to study of the regularity of solutions to elliptic PDEs. The aim of this paper is trying to bring together these two areas and this paper is intended as an attempt at motivating some further research on these areas. A version of Morrey space associated with Karamata regular variation is introduced. As application, some estimates of operators, especially one-sided operators, on these spaces are considered. Jiajia Wang, Zunwei Fu, Shaoguang Shi, and Ling Mi Copyright © 2017 Jiajia Wang et al. All rights reserved. Odd Periodic Solutions of Fully Second-Order Ordinary Differential Equations with Superlinear Nonlinearities Wed, 23 Aug 2017 00:00:00 +0000 This paper is concerned with the existence of periodic solutions for the fully second-order ordinary differential equation , , where the nonlinearity is continuous and is -periodic in . Under certain inequality conditions that may be superlinear growth on , an existence result of odd -periodic solutions is obtained via Leray-Schauder fixed point theorem. Yongxiang Li and Lanjun Guo Copyright © 2017 Yongxiang Li and Lanjun Guo. All rights reserved. On the Existence of Positive Solutions for a Fourth-Order Boundary Value Problem Mon, 14 Aug 2017 06:09:41 +0000 By using the method of order reduction and the fixed point index, the existence of positive solutions for a fourth-order boundary value problem is studied. We provide conditions under which the existence results hold. Such conditions are related to the first eigenvalue corresponding to the relevant linear differential equation with dependence on the derivatives of unknown function. Yumei Zou Copyright © 2017 Yumei Zou. All rights reserved. A New Nonsmooth Bundle-Type Approach for a Class of Functional Equations in Hilbert Spaces Tue, 08 Aug 2017 06:20:16 +0000 A new bundle-type approach for solving a class of functional equations is presented by combining bundle idea for nonsmooth optimization with common iterative process for functional equations. Our strategy is to approximate the nonsmooth function in functional equation by a sequence of convex piecewise linear functions, as in the bundle method; this makes the problem more tractable and reduces the difficulty of implementation of method. We only require the piecewise linear convex approximate functions, rather than the actual function, to satisfy the uniform boundedness condition with respect to one variable at stability centers. One example is given to demonstrate the application of the proposed method. Jie Shen, Miao Tian, Fang-Fang Guo, and Jun-Nan Zhang Copyright © 2017 Jie Shen et al. All rights reserved. Lipschitz-Type and Bloch-Type Spaces of Pluriharmonic Mappings in a Hilbert Space Mon, 07 Aug 2017 09:35:43 +0000 We investigate some properties of pluriharmonic mappings in an infinite dimensional complex Hilbert space. Several characterizations for pluriharmonic mappings to be in Lipschitz-type and Bloch-type spaces are given, which are generalizations of the corresponding known ones for holomorphic functions with several complex variables. Yong Liu Copyright © 2017 Yong Liu. All rights reserved. Jordan -Derivations on Operator Algebras Tue, 01 Aug 2017 00:00:00 +0000 Let be a CSL subalgebra of a von Neumann algebra acting on a Hilbert space . It is shown that any Jordan -derivation on is an -derivation, where are any automorphisms on . Moreover, the th power -maps on are investigated. Quanyuan Chen, Xiaochun Fang, and Changjing Li Copyright © 2017 Quanyuan Chen et al. All rights reserved. Metric Projection Operator and Continuity of the Set-Valued Metric Generalized Inverse in Banach Spaces Mon, 31 Jul 2017 00:00:00 +0000 In this paper, continuous homogeneous selection and continuity for the set-valued metric generalized inverses in 3-strictly convex spaces are investigated by continuity of metric projection. The results are an answer to the problem posed by Nashed and Votruba. Moreover, authors prove that there exists a proximinal hyperplane such that is continuous and is not approximative compact. Shaoqiang Shang and Jingxin Zhang Copyright © 2017 Shaoqiang Shang and Jingxin Zhang. All rights reserved. S-Shaped Connected Component for Nonlinear Fourth-Order Problem of Elastic Beam Equation Mon, 24 Jul 2017 09:24:31 +0000 We investigate the existence of -shaped connected component in the set of positive solutions of the fourth-order boundary value problem: , , where is a parameter, , and with . We develop a bifurcation approach to deal with this extreme situation by constructing a sequence of functions satisfying and By studying the auxiliary problems, we get a sequence of unbounded connected components , and, then, we find an unbounded connected component in the set of positive solutions of the fourth-order boundary value problem which satisfies and is -shaped. Jinxiang Wang, Ruyun Ma, and Jin Wen Copyright © 2017 Jinxiang Wang et al. All rights reserved. Precompact Sets, Boundedness, and Compactness of Commutators for Singular Integrals in Variable Morrey Spaces Thu, 20 Jul 2017 00:00:00 +0000 We give sufficient conditions for subsets to be precompact sets in variable Morrey spaces. Then we obtain the boundedness of the commutator generated by a singular integral operator and a BMO function on the variable Morrey spaces. Finally, we discuss the compactness of the commutator generated by a singular integral operator and a BMO function on the variable Morrey spaces. Wei Wang and Jingshi Xu Copyright © 2017 Wei Wang and Jingshi Xu. All rights reserved. Hyperstability of Some Functional Equations on Restricted Domain Sun, 16 Jul 2017 00:00:00 +0000 The paper concerns functions which approximately satisfy, not necessarily on the whole linear space, a generalization of linear functional equation. A Hyers-Ulam stability result is proved and next applied to give conditions implying the hyperstability of the equation. The results may be used as tools in stability studies on restricted domains for various functional equations. We use the main theorem to obtain a few hyperstability results of Fréchet equation on restricted domain for different control functions. Anna Bahyrycz and Jolanta Olko Copyright © 2017 Anna Bahyrycz and Jolanta Olko. All rights reserved. A New Kind of Weak Solution of Non-Newtonian Fluid Equation Thu, 13 Jul 2017 09:35:37 +0000 If the non-Newtonian fluid equation with a diffusion coefficient is degenerate on the boundary, the weak solution lacks the regularity to define the trace on the boundary. By introducing a new kind of weak solutions, the stability of the solutions is established without any boundary condition. Huashui Zhan and Bifen Xu Copyright © 2017 Huashui Zhan and Bifen Xu. All rights reserved. Best -Simultaneous Approximation in   Wed, 12 Jul 2017 00:00:00 +0000 Let be a Banach space. Let and denote by the Banach space of all -valued Bochner -integrable functions on a certain positive complete -finite measure space , endowed with the usual -norm. In this paper, the theory of lifting is used to prove that, for any weakly compact subset of , the set is -simultaneously proximinal in for any arbitrary monotonous norm in . Tijani Pakhrou Copyright © 2017 Tijani Pakhrou. All rights reserved. Existence of Solutions for a Class of Coupled Fractional Differential Systems with Nonlocal Boundary Conditions Thu, 06 Jul 2017 06:56:00 +0000 Applying Schauder fixed point theorem and Leray-Schauder nonlinear alternative theory, this paper is concerned with the existence of solutions to coupled fractional differential systems with fractional integral boundary value conditions. Meanwhile, two examples are worked out to illustrate the application of the main results. Tingting Qi, Yansheng Liu, and Yujun Cui Copyright © 2017 Tingting Qi et al. All rights reserved. Isometries of Spaces of Radon Measures Tue, 04 Jul 2017 07:01:59 +0000 Let and denote a compact metrizable space with and the unit interval, respectively. We prove Milutin and Cantor-Bernstein type theorems for the spaces of Radon measures on compact Hausdorff spaces . In particular, we obtain the following results: () for every infinite closed subset of the spaces , , and are order-isometric; () for every discrete space with the spaces and are order-isometric, whereas there is no linear homeomorphic injection from into . Marek Wójtowicz Copyright © 2017 Marek Wójtowicz. All rights reserved. Positive Solutions for Singular Semipositone Fractional Differential Equation Subject to Multipoint Boundary Conditions Sun, 02 Jul 2017 07:03:44 +0000 Existence result together with multiplicity result of positive solutions of higher-order fractional multipoint boundary value problems is given by considering the integrations of height functions on some special bounded sets. The nonlinearity may change its sign and may possess singularities on the time and the space variables at the same time. Rui Pu, Xingqiu Zhang, Yujun Cui, Peilong Li, and Weiwei Wang Copyright © 2017 Rui Pu et al. All rights reserved. Approximate Controllability for Functional Equations with Riemann-Liouville Derivative by Iterative and Approximate Method Tue, 27 Jun 2017 09:37:21 +0000 We discuss the functional control systems governed by differential equations with Riemann-Liouville fractional derivative in general Banach spaces in the present paper. First we derive the uniqueness and existence of mild solutions for functional differential equations by the approach of fixed point and fractional resolvent under more general settings. Then we present new sufficient conditions for approximate controllability of functional control system by means of the iterative and approximate method. Our results unify and generalize some previous works on this topic. Badawi Hamza Elbadawi Ibrahim, Zhenbin Fan, and Gang Li Copyright © 2017 Badawi Hamza Elbadawi Ibrahim et al. All rights reserved. Hardy-Sobolev Spaces Associated with Twisted Convolution Wed, 21 Jun 2017 08:43:51 +0000 We first define the Hardy-Sobolev spaces associated with twisted convolution; then we give the atomic decomposition. As an application, we consider the endpoint version of the div-curl theorem for the twisted convolution. Jizheng Huang, Weiwei Li, and Yaqiong Wang Copyright © 2017 Jizheng Huang et al. All rights reserved. The Characteristic Properties of the Minimal -Mean Width Tue, 20 Jun 2017 09:42:48 +0000 Giannopoulos proved that a smooth convex body has minimal mean width position if and only if the measure , supported on , is isotropic. Further, Yuan and Leng extended the minimal mean width to the minimal -mean width and characterized the minimal position of convex bodies in terms of isotropicity of a suitable measure. In this paper, we study the minimal -mean width of convex bodies and prove the existence and uniqueness of the minimal -mean width in its images. In addition, we establish a characterization of the minimal -mean width, conclude the average with a variation of the minimal -mean width position, and give the condition for the minimum position of . Tongyi Ma Copyright © 2017 Tongyi Ma. All rights reserved. A New Generalization on Cauchy-Schwarz Inequality Tue, 13 Jun 2017 10:07:38 +0000 We extend the well-known Cauchy-Schwarz inequality involving any number of real or complex functions and also give a necessary and sufficient condition for the equality. This is another generalized version of the Cauchy-Schwarz inequality. Songting Yin Copyright © 2017 Songting Yin. All rights reserved. On a Fourth-Order Boundary Value Problem at Resonance Sun, 11 Jun 2017 00:00:00 +0000 We investigate the spectrum structure of the eigenvalue problem . As for the application of the spectrum structure, we show the existence of solutions of the fourth-order boundary value problem at resonance , which models a statically elastic beam with both end-points being cantilevered or fixed, where is the first eigenvalue of the corresponding eigenvalue problem and nonlinearity may be unbounded. Man Xu and Ruyun Ma Copyright © 2017 Man Xu and Ruyun Ma. All rights reserved. Diffusion Convection Equation with Variable Nonlinearities Thu, 01 Jun 2017 06:13:42 +0000 The paper studies diffusion convection equation with variable nonlinearities and degeneracy on the boundary. Unlike the usual Dirichlet boundary value, only a partial boundary value condition is imposed. If there are some restrictions in the diffusion coefficient, the stability of the weak solution based on the partial boundary value condition is obtained. In general, we may obtain a local stability of the weak solutions without any boundary value condition. Huashui Zhan Copyright © 2017 Huashui Zhan. All rights reserved.