http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/484879.htmlThe purpose of this work is to investigate the uniqueness and existence of local solutions for the boundary value problem of a quasilinear parabolic equation. The result is obtained via the abstract theory of maximal regularity. Applications are given to some model problems in nonstationary radiative heat transfer and reaction-diffusion equation with nonlocal boundary flux conditions.Yuandi Wang and Shengzhou Zheng© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/834158.htmlWe consider a multi-point boundary value problem on the half-line with impulses. By using a fixed-point theorem due to Avery and Peterson, the existence of at least three positive solutions is obtained.Jianli Li and Juan J. Nieto© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/532546.htmlWe consider a similinear elliptic equation with sign-changing potential −Δu−V(x)u=f(x,u), u∈H1(ℝN), where V(x) is a function possibly changing sign in ℝN. Under certain assumptions on f, we prove that the equation has infinitely many solutions.Chen Yu and Li Yongqing© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/540863.htmlWe present some recent existence results for second-order singular periodic differential equations. A nonlinear alternative principle of Leray-Schauder type, a well-known fixed point theorem in cones, and Schauder's fixed point theorem are used in the proof. The results shed some light on the differences between a strong singularity and a weak singularity.Jifeng Chu and Juan J. Nieto© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/584203.htmlWe study existence and multiplicity of positive solutions for the following Dirichlet equations: −Δu−(μ/|x|2)u=λf(x)|u|q−2u+g(x)|u|2∗−2u in Ω, u=0 on ∂Ω, where 0∈Ω⊂ℝN(N≥3) is a bounded domain with smooth boundary ∂Ω, λ>0, 0≤μ<μ¯=(N−2)2/4, 2∗=2N/(N−2), 1≤q<2, and f, g are continuous functions on Ω¯ which are somewhere positive but which may change sign on Ω.Tsing-San Hsu and Huei-Li Lin© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/625347.htmlWe study the existence of solutions for a class of fractional differential inclusions with anti-periodic boundary conditions. The main result of the paper is based on Bohnenblust-Karlins fixed point theorem. Some applications of the main result are also discussed.Bashir Ahmad and Victoria Otero-Espinar© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/820237.htmlWe consider a nonlinear elliptic equation driven by the p-Laplacian with a nonsmooth potential (hemivariational inequality) and Dirichlet boundary condition. Using a variational approach based on nonsmooth critical point theory together with the method of upper and lower solutions, we prove the existence of at least three nontrivial smooth solutions: one positive, the second negative, and the third sign changing (nodal solution). Our hypotheses on the nonsmooth potential incorporate in our framework of analysis the so-called asymptotically p-linear problems.Ravi P. Agarwal, Michael E. Filippakis, Donal O'Regan, and Nikolaos S. Papageorgiou© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/568657.htmlThe pulsatile flow of blood through stenosed arteries is analyzed by assuming the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a non-Newtonian fluid and the plasma in the peripheral layer as a Newtonian fluid. The non-Newtonian fluid in the core region of the artery is assumed as a (i) Herschel-Bulkley fluid and (ii) Casson fluid. Perturbation method is used to solve the resulting system of non-linear partial differential equations. Expressions for various flow quantities are obtained for the two-fluid Casson model. Expressions of the flow quantities obtained by Sankar and Lee (2006) for the two-fluid Herschel-Bulkley model are used to get the data for comparison. It is found that the plug flow velocity and velocity distribution of the two-fluid Casson model are considerably higher than those of the two-fluid Herschel-Bulkley model. It is also observed that the pressure drop, plug core radius, wall shear stress and the resistance to flow are significantly very low for the two-fluid Casson model than those of the two-fluid Herschel-Bulkley model. Hence, the two-fluid Casson model would be more useful than the two-fluid Herschel-Bulkley model to analyze the blood flow through stenosed arteries.D. S. Sankar and Ahmad Izani Md. Ismail© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/103276.htmlWe present sufficient conditions for the existence of at least twin or triple positive solutions of a nonlinear four-point singular boundary value problem with a p-Laplacian dynamic equation on a time scale. Our results are obtained via some new multiple fixed point theorems.Shihuang Hong© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/260941.htmlWe consider an axisymmetric inverse heat conduction problem of determining the surface temperature from a fixed location inside a cylinder. This problem is ill-posed; the solution (if it exists) does not depend continuously on the data. A special project method—dual least squares method generated by the family of Shannon wavelet is applied to formulate regularized solution. Meanwhile, an order optimal error estimate between the approximate solution and exact solution is proved.Wei Cheng and Chu-Li Fu© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/540360.htmlIn this paper, we establish two different existence results of solutions for a nonlocal elliptic equations with nonlinear boundary condition. The first one is based on Galerkin method, and gives a priori estimate. The second one is based on Mountain Pass Lemma.Fanglei Wang and Yukun An© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2008/742030.htmlWe show the existence of a nontrivial solution for a class of the systems of the superquadratic nonlinear wave equations with Dirichlet boundary conditions and periodic conditions with a superquadratic nonlinear terms at infinity which have continuous derivatives. We approach the variational method and use the critical point theory which is the Linking Theorem for the strongly indefinite corresponding functional.Tacksun Jung and Q-Heung Choi© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/509801.htmlBy introducing a compactness lemma and considering a constrained variational problem, we obtain a set Gℝ2 of steady waves for Hasegawa-Mima equation, which describes the motion of drift waves in plasma. Moreover, we prove that Gℝ2 is a stable set for the initial value problem of the equation, in the sense that a solution ψ(t) which starts near Gℝ2 will remain near it for all time.Boling Guo and Daiwen Huang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/791548.htmlBy appropriate bounding function pair and modified functions, using the theory of differential inequalities, this paper presents the existence and location criteria of solutions for the system of general nth-order differential equations with nonlinear boundary conditions. We give an example showing that the results are sharp. Our results extend many existing results.Li Sun, Mingru Zhou, and Guangwa Wang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/708576.htmlThis paper deals with some existence results for a boundary value problem involving a nonlinear integrodifferential equation of fractional order q∈(1,2] with integral boundary conditions. Our results are based on contraction mapping principle and Krasnosel'skiĭ's fixed point theorem.Bashir Ahmad and Juan J. Nieto© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/670675.htmlThe existence of infinitely many solutions for a Sturm-Liouville boundary value problem, under an appropriate oscillating behavior of the possibly discontinuous nonlinear term, is obtained. Several special cases and consequences are pointed out and some examples are presented. The technical approach is mainly based on a result of infinitely many critical points for locally Lipschitz functions.Gabriele Bonanno and Giovanni Molica Bisci© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/305291.htmlThe present paper deals with the inverse problem for linear elliptic equations of second order from Dirichlet to Neumann map in multiply connected domains. Firstly the formulation and the complex form of the problem for the equations are given, and then the existence and global uniqueness of solutions for the above problem are proved by the complex analytic method, where we absorb the advantage of the methods in previous works and give some improvement and development.Guochun Wen, Zuoliang Xu, and Fengmin Yang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2008/192353.htmlGlobal behaviors and optimal harvesting of a class of impulsive periodic logistic single-species system with continuous periodic control strategy is investigated. Four new sufficient conditions that guarantee the exponential stability of the impulsive evolution operator introduced by us are given. By virtue of exponential stability of the impulsive evolution operator, we present the existence, uniqueness and global asymptotical stability of periodic solutions. Further, the existence result of periodic optimal controls for a Bolza problem is given. At last, an academic example is given for demonstration.JinRong Wang, X. Xiang, and W. Wei© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2008/437453.htmlWe study the boundary value problem for a kind N-dimension nonlinear fractional differential system with the nonlinear terms involved in the fractional derivative explicitly. The fractional differential operator here is the standard Riemann-Liouville differentiation. By means of fixed point theorems, the existence and multiplicity results of positive solutions are received. Furthermore, two examples given here illustrate that the results are almost sharp.Aijun Yang and Weigao Ge© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2008/585378.htmlWe consider a second-order ordinary differential equation with antiperiodic boundary conditions and impulses. By using Schaefer's fixed-point theorem, some existence results are obtained.Chuanzhi Bai© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2008/279410.htmlThe classic Kalman filtering equations for independent and correlated white noises are ordinary differential equations (deterministic or stochastic) with the respective initial conditions. Changing the noise processes by taking them to be more realistic wide band noises or delayed white noises creates challenging partial differential equations with initial and boundary conditions. In this paper, we are aimed to give a survey of this connection between Kalman filtering and boundary value problems, bringing them into the attention of mathematicians as well as engineers dealing with Kalman filtering and boundary value problems.Agamirza Bashirov, Zeka Mazhar, and Sinem Ertürk© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2008/189748.htmlAn initial-boundary value problem for 1D flow of a compressible viscous heat-conducting micropolar fluid is considered; the fluid is thermodynamically perfect and polytropic. Assuming that the initial data are Hölder continuous on ]0,1[ and transforming the original problem into homogeneous one, we prove that the state function is Hölder continuous on ]0,1[×]0,T[, for each T>0. The proof is based on a global-in-time existence theorem obtained in the previous research paper and on a theory of parabolic equations.Nermina Mujaković© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2008/864297.htmlWe prove existence results for second-order impulsive differential equations with antiperiodic boundary value conditions in the presence of classical fixed point theorems. We also obtain the expression of Green's function of related linear operator in the space of piecewise continuous functions.Yepeng Xing and Valery Romanovski© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2008/425256.htmlWe consider Hölder continuous circulant (2×2) matrix functions G21 defined on the Ahlfors-David regular boundary Γ of a domain Ω in ℝ2n. The main goal is to study under which conditions such a function G21 can be decomposed as G21=G21+-G21-, where the components G21± are extendable to two-sided H-monogenic functions in the interior and the exterior of Ω, respectively. H-monogenicity is a concept from the framework of Hermitean Clifford analysis, a higher dimensional function theory centered around the simultaneous null solutions of two first-order vector-valued differential operators, called Hermitean Dirac operators. H-monogenic functions then are the null solutions of a (2×2) matrix Dirac operator, having these Hermitean Dirac operators as its entries; such functions have been crucial for the development of function theoretic results in the Hermitean Clifford context.Ricardo Abreu Blaya, Juan Bory Reyes, Fred Brackx, Bram De Knock, Hennie De Schepper, Dixan Peña Peña, and Frank Sommen© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2008/937138.htmlThis paper deals with the existence of solutions of the periodic boundary value problem of the impulsive Duffing equations: x′′(t)+αx′(t)+βx(t)=f(t,x(t),x(α1(t)),…,x(αn(t))), a.e.  t∈[0,T], Δx(tk)=Ik(x(tk),x′(tk)), k=1, …,m, Δx′(tk)=Jk(x(tk),x′(tk)), k=1,…,m, x(i)(0)=x(i)(T), i=0,1. Sufficient conditions are established for the existence of at least one solution of above-mentioned boundary value problem. Our method is based upon Schaeffer's fixed-point theorem. Examples are presented to illustrate the efficiency of the obtained results.Xingyuan Liu and Yuji Liu© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2008/403761.htmlExistence and multiplicity results for nodal solutions are obtained for the fourth-order boundary value problem (BVP) u(4)(t)=f(t,u(t)), 0<t<1, u(0)=u(1)=u′′(0)=u′′(1)=0, where f:[0,1]×R→R is continuous. The critical point theory and admissible invariant sets are employed to discuss this problem.Yang Yang, Jihui Zhang, and Zhitao Zhang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2008/457028.htmlPositive solutions to the singular initial-boundary value problems x′′=−f(t, xt), 0<t<1, x0=0, x(1)=0, are obtained by applying the Schauder fixed-point theorem, where xt(u)=x(t+u) (0≤t≤1) on [−r,0] and f(⋅,⋅):(0,1)×(C+\{0})→R+(C+={x∈C([−r,0],R), x(t)≥0, ∀t∈[−r,0]}) may be singular at φ(u)=0 (−r≤u≤0) and t=0. As an application, an example is given to demonstrate our result.Fengfei Jin and Baoqiang Yan© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2008/197205.htmlSome multiplicity results for solutions of an impulsive boundary value problem are obtained under the condition of non-well-ordered upper and lower solutions. The main ideas of this paper are to associate a Leray-Schauder degree with the lower or upper solution.Xu Xian, Donal O'Regan, and R. P. Agarwal© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2008/752827.htmlThis paper is concerned with the existence and uniqueness of solutions for the second-order nonlinear delay differential equations. By the use of the Schauder fixed point theorem, the existence of the solutions on the half-line is derived. Via the Banach contraction principle, another result concerning the existence and uniqueness of solutions on the half-line is established. The main results in this paper extend some of the existing literatures.Yuming Wei© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2008/901503.htmlThis paper is concerned with the study of the Dirichlet problem for a class of second-order linear elliptic equations in weighted Sobolev spaces on unbounded domains of ℝn, n≥3. We state a regularity result and we can deduce an existence and uniqueness theorem.Serena Boccia, Sara Monsurrò, and Maria Transirico© 2009, Hindawi Publishing Corporation. All rights reserved.