http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2012, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2011/190548/We show that the energy to the thermoelastic transmission problem decays exponentially as time goes to infinity. We also prove the existence, uniqueness, and regularity of the solution to the system.Margareth S. Alves, Jaime E. Muñoz Rivera, Mauricio Sepúlveda, and Octavio Vera VillagránCopyright © 2011 Margareth S. Alves et al. All rights reserved.http://www.hindawi.com/journals/bvp/2011/475126/Though boundary value problems for fractional differential equations have been extensively studied, most of the studies focus on scalar equations and the fractional order between 1 and 2. On the other hand, delay is natural in practical systems. However, not much has been done for fractional differential equations with delays. Therefore, in this paper, we consider a boundary value problem of a general delayed nonlinear fractional system. With the help of some fixed point theorems and the properties of the Green function, we establish several sets of sufficient conditions on the existence of positive solutions. The obtained results extend and include some existing ones and are illustrated with some examples for their feasibility.Zigen Ouyang, Yuming Chen, and Shuliang ZouCopyright © 2011 Zigen Ouyang et al. All rights reserved.http://www.hindawi.com/journals/bvp/2011/569191/The aim of this paper is to study a fourth-order separated boundary value problem with the right-hand side function satisfying one-sided Nagumo-type condition. By making a series of a priori estimates and applying lower and upper functions techniques and Leray-Schauder degree theory, the authors obtain the existence and location result of solutions to the problem.Wenjing Song and Wenjie GaoCopyright © 2011 Wenjing Song and Wenjie Gao. All rights reserved.http://www.hindawi.com/journals/bvp/2011/516481/We study a boundary value problem to Langevin equation involving two fractional orders. The Banach fixed point theorem and Krasnoselskii's fixed point theorem are applied to establish the existence results.Anping Chen and Yi ChenCopyright © 2011 Anping Chen and Yi Chen. All rights reserved.http://www.hindawi.com/journals/bvp/2011/875057/Green's function G(x,y) of the clamped boundary value problem for the differential operator -1Md/dx2M on the interval (−s,s) is obtained. The best constant of corresponding Sobolev inequality is given by max|y|≤sG(y,y). In addition, it is shown that a reverse of the Sobolev best constant is the one which appears in the generalized Lyapunov inequality by Das and Vatsala (1975).Kohtaro Watanabe, Yoshinori Kametaka, Hiroyuki Yamagishi, Atsushi Nagai, and Kazuo TakemuraCopyright © 2011 Kohtaro Watanabe et al. All rights reserved.http://www.hindawi.com/journals/bvp/2011/829543/A new formula expressing explicitly the derivatives of Bernstein polynomials of any degree and for any order in terms of Bernstein polynomials themselves is proved, and a formula expressing the Bernstein coefficients of the general-order derivative of a differentiable function in terms of its Bernstein coefficients is deduced. An application of how to use Bernstein polynomials for solving high even-order differential equations by Bernstein Galerkin and Bernstein Petrov-Galerkin methods is described. These two methods are then tested on examples and compared with other methods. It is shown that the presented methods yield better results.E. H. Doha, A. H. Bhrawy, and M. A. SakerCopyright © 2011 E. H. Doha et al. All rights reserved.http://www.hindawi.com/journals/bvp/2011/483057/By using the cone theory and the Banach contraction mapping principle, the existence and uniqueness results are established for singular third-order boundary value problems. The theorems obtained are very general and complement previous known results.Peiguo ZhangCopyright © 2011 Peiguo Zhang. All rights reserved.http://www.hindawi.com/journals/bvp/2011/192156/We study periodic solutions for nonlinear second-order ordinary differential problem x′′+f(t,x,x′)=0. By constructing upper and lower boundaries and using Leray-Schauder degree theory, we present a result about the existence and uniqueness of a periodic solution for second-order ordinary differential equations with some assumption.Jian ZuCopyright © 2011 Jian Zu. All rights reserved.http://www.hindawi.com/journals/bvp/2011/128614/We study the incompressible magneto-micropolar fluid equations with partial viscosity in ℝn (n=2,3). A blow-up criterion of smooth solutions is obtained. The result is analogous to the celebrated Beale-Kato-Majda type criterion for the inviscid Euler equations of incompressible fluids.Yu-Zhu Wang, Liping Hu, and Yin-Xia WangCopyright © 2011 Yu-Zhu Wang et al. All rights reserved.http://www.hindawi.com/journals/bvp/2011/172818/By using critical point theory, Lyapunov-Schmidt reduction method, and characterization of the Brouwer degree of critical points, sufficient conditions to guarantee the existence of five or six solutions together with their sign properties to discrete second-order two-point boundary value problem are obtained. An example is also given to demonstrate our main result.Bo Zheng, Huafeng Xiao, and Haiping ShiCopyright © 2011 Bo Zheng et al. All rights reserved.http://www.hindawi.com/journals/bvp/2011/404696/This paper deals with a predator-prey model with Beddington-DeAngelis functional response under homogeneous Neumann boundary conditions. We mainly discuss the following three problems: (1) stability of the nonnegative constant steady states for the reaction-diffusion system; (2) the existence of Turing patterns; (3) the existence of stationary patterns created by cross-diffusion.Lina Zhang and Shengmao FuCopyright © 2011 Lina Zhang and Shengmao Fu. All rights reserved.http://www.hindawi.com/journals/bvp/2011/736093/Using the variational principle of Ricceri and a local mountain pass lemma, we study the existence of three distinct solutions for the following resonant Duffing-type equations with damping and perturbed term u″(t)+σu'(t)+f(t,u(t))+λg(t,u(t))=p(t), a.e. t∈[0,ω], u(0)=0=u(ω) and without perturbed term u″(t)+σu'(t)+f(t,u(t))=p(t), a.e. t∈[0,ω], u(0)=0=u(ω).Yongkun Li and Tianwei ZhangCopyright © 2011 Yongkun Li and Tianwei Zhang. All rights reserved.http://www.hindawi.com/journals/bvp/2011/214289/We discuss Neumann and Robin problems driven by the p-Laplacian with jumping nonlinearities. Using sub-sup solution method, Fucík spectrum, mountain pass theorem, degree theorem together with suitable truncation techniques, we show that the Neumann problem has infinitely many nonconstant solutions and the Robin problem has at least four nontrivial solutions. Furthermore, we study oscillating equations with Robin boundary and obtain infinitely many nontrivial solutions.Jing Zhang and Xiaoping XueCopyright © 2011 Jing Zhang and Xiaoping Xue. All rights reserved.http://www.hindawi.com/journals/bvp/2011/138396/This paper is concerned with the structure of the weak entropy solutions to two-dimension Riemann initial-boundary value problem with curved boundary. Firstly, according to the definition of weak entropy solution in the sense of Bardos-Leroux-Nedelec (1979), the necessary and sufficient condition of the weak entropy solutions with piecewise smooth is given. The boundary entropy condition and its equivalent formula are proposed. Based on Riemann initial value problem, weak entropy solutions of Riemann initial-boundary value problem are constructed, the behaviors of solutions are clarified, and we focus on verifying that the solutions satisfy the boundary entropy condition. For different Riemann initial-boundary value data, there are a total of five different behaviors of weak entropy solutions. Finally, a worked-out specific example is given.Huazhou Chen and Tao PanCopyright © 2011 Huazhou Chen and Tao Pan. All rights reserved.http://www.hindawi.com/journals/bvp/2011/268032/The boundary value problems for degenerate anisotropic differential operator equations with variable coefficients are studied. Several conditions for the separability and Fredholmness in Banach-valued Lp spaces are given. Sharp estimates for resolvent, discreetness of spectrum, and completeness of root elements of the corresponding differential operators are obtained. In the last section, some applications of the main results are given.Ravi Agarwal, Donal O'Regan, and Veli ShakhmurovCopyright © 2011 Ravi Agarwal et al. All rights reserved.http://www.hindawi.com/journals/bvp/2011/594128/This paper investigates the eigenvalue problem for a class of singular elastic beam equations where one end is simply supported and the other end is clamped by sliding clamps. Firstly, we establish a necessary and sufficient condition for the existence of positive solutions, then we prove that the closure of positive solution set possesses an unbounded connected branch which bifurcates from (0,θ). Our nonlinearity f(t,u,v,w) may be singular at u,v,  t=0 and/or t=1.Huiqin LuCopyright © 2011 Huiqin Lu. All rights reserved.http://www.hindawi.com/journals/bvp/2011/827510/We consider the existence, multiplicity of positive solutions for the integral boundary value problem with ϕ-Laplacian (ϕ(u'(t)))'+f(t,u(t),u'(t))=0, t∈[0,1], u(0)=∫01u(r)g(r)dr, u(1)=∫01u(r)h(r)dr, where ϕ is an odd, increasing homeomorphism from R onto R. We show that it has at least one, two, or three positive solutions under some assumptions by applying fixed point theorems. The interesting point is that the nonlinear term f is involved with the first-order derivative explicitly.Yonghong DingCopyright © 2011 Yonghong Ding. All rights reserved.http://www.hindawi.com/journals/bvp/2011/743135/This paper generalises the work done in Currie and Love (2010), where we studied the effect of applying two Crum-type transformations to a weighted second-order difference equation with various combinations of Dirichlet, non-Dirichlet, and affine λ-dependent boundary conditions at the end points, where λ is the eigenparameter. We now consider general λ-dependent boundary conditions. In particular we show, using one of the Crum-type transformations, that it is possible to go up and down a hierarchy of boundary value problems keeping the form of the second-order difference equation constant but possibly increasing or decreasing the dependence on λ of the boundary conditions at each step. In addition, we show that the transformed boundary value problem either gains or loses an eigenvalue, or the number of eigenvalues remains the same as we step up or down the hierarchy.Sonja Currie and Anne D. LoveCopyright © 2011 Sonja Currie and Anne D. Love. All rights reserved.http://www.hindawi.com/journals/bvp/2011/297026/The method of upper and lower solutions and the Schauder fixed point theorem are used to investigate the existence and uniqueness of a positive solution to a singular boundary value problem for a class of nonlinear fractional differential equations with non-monotone term. Moreover, the existence of maximal and minimal solutions for the problem is also given.Changyou Wang, Ruifang Wang, Shu Wang, and Chunde YangCopyright © 2011 Changyou Wang et al. All rights reserved.http://www.hindawi.com/journals/bvp/2011/845413/We study the following second-order differential equation: (Φp(x'))'+F(x,t)x'+ωpΦp(x)+α|x|lx+e(x,t)=0, where Φp(s)=|s|(p-2)s  (p>1), α>0 and ω>0 are positive constants, and l satisfies -1<l<p-2. Under some assumptions on the parities of F(x,t) and e(x,t), by a small twist theorem of reversible mapping we obtain the existence of quasiperiodic solutions and boundedness of all the solutions.Shunjun Jiang, Junxiang Xu, and Fubao ZhangCopyright © 2011 Shunjun Jiang et al. All rights reserved.http://www.hindawi.com/journals/bvp/2010/368169/We investigate the existence of positive solutions of singular problem (-1)mx(2m+1)=f(t,x,…,x(2m)), x(0)=0, x(2i-1)(0)=x(2i-1)(T)=0, 1≤i≤m. Here, m≥1 and the Carathéodory function f(t,x0,…,x2m) may be singular in all its space variables x0,…,x2m. The results are proved by regularization and sequential techniques. In limit processes, the Vitali convergence theorem is used.Ravi P. Agarwal, Donal O'Regan, and Svatoslav StaněkCopyright © 2010 Ravi P. Agarwal et al. All rights reserved.http://www.hindawi.com/journals/bvp/2010/471491/The existence and uniqueness of a slowly oscillating solution to parabolic inverse problems for a type of boundary value problem are established. Stability of the solution is discussed.Fenglin Yang and Chuanyi ZhangCopyright © 2010 Fenglin Yang and Chuanyi Zhang. All rights reserved.http://www.hindawi.com/journals/bvp/2010/526917/The paper is devoted to the study of an initial boundary value problem for a linear second-order differential system with constant coefficients. The first part of the paper is concerned with the existence of the solution to a boundary value problem for the second-order differential system, in the strip ΩA=Rd−1×(0,A), where A is a suitable positive number. The result is proved by means of the same procedure followed in a previous paper to study the related initial value problem. Subsequently, we consider a mixed problem for the second-order constant coefficient system, where the space variable varies in ΩA and the time-variable belongs to the bounded interval ]0,T[, with T sufficiently small in order that the operator satisfies suitable energy estimates. We obtain by superposition the existence of a solution u∈L2([0,T]×[0,A],H3(Rd−1)), by studying two related mixed problems, whose solutions exist due to the results proved for the Cauchy problem in a previous paper and for the boundary value problem in the first part of this paper.Rita CavazzoniCopyright © 2010 Rita Cavazzoni. All rights reserved.http://www.hindawi.com/journals/bvp/2010/363518/We deal with a perturbed eigenvalue Dirichlet-type problem for an elliptic hemivariational inequality involving the p-Laplacian. We show that an appropriate oscillating behaviour of the nonlinear part, even under small perturbations, ensures the existence of infinitely many solutions. The main tool in order to obtain our abstract results is a recent critical-point theorem for nonsmooth functionals.Giuseppina D'Aguì and Giovanni Molica BisciCopyright © 2010 Giuseppina D'Aguì and Giovanni Molica Bisci. All rights reserved.http://www.hindawi.com/journals/bvp/2010/268946/By using variational methods, we study the multiplicity of solutions for Kirchhoff type problems −(a+b∫Ω|∇u|2)Δu=f(x,u), in Ω; u=0, on ∂Ω. Existence results of two nontrivial solutions and infinite many solutions are obtained.Bitao Cheng, Xian Wu, and Jun LiuCopyright © 2010 Bitao Cheng et al. All rights reserved.http://www.hindawi.com/journals/bvp/2010/607453/We study the existence and nonexistence of solutions for the singular quasilinear problem -div(|x|-ap|∇u|p-2∇u)=h(x)f(u)+λH(x)g(u), x∈RN, u(x)>0, x∈RN, lim⁡|x|→∞u(x)=0, where 1<p<N, 0≤a<(N−p)/p and f(u)  and  g(u) behave like um and un with 0<m≤p-1<n at the origin. We obtain the existence by the upper and lower solution method and the nonexistence by the test function method.Caisheng Chen, Zhenqi Wang, and Fengping WangCopyright © 2010 Caisheng Chen et al. All rights reserved.http://www.hindawi.com/journals/bvp/2010/524862/Assume that q is a positive continuous function in ℝN and satisfies the suitable conditions. We prove that the Dirichlet problem −Δu+u=q(z)|u|p−2u admits at least three positive solutions in an exterior domain.Tsing-San Hsu and Huei-Li LinCopyright © 2010 Tsing-San Hsu and Huei-Li Lin. All rights reserved.http://www.hindawi.com/journals/bvp/2010/853717/By means of the two-scale convergence method, we investigate the asymptotic behavior of eigenvalues and eigenfunctions of Stekloff eigenvalue problems in perforated domains. We prove a concise and precise homogenization result including convergence of gradients of eigenfunctions which improves the understanding of the asymptotic behavior of eigenfunctions. It is also justified that the natural local problem is not an eigenvalue problem.Hermann DouanlaCopyright © 2010 Hermann Douanla. All rights reserved.http://www.hindawi.com/journals/bvp/2010/429813/The paper studies the singular differential equation (p(t)u')'=p(t)f(u), which has a singularity at t=0. Here the existence of strictly increasing solutions satisfying sup⁡{|u(t)|:t∈[0,∞)}≥L>0 is proved under the assumption that f has two zeros 0 and L and a superlinear behaviour near -∞. The problem generalizes some models arising in hydrodynamics or in the nonlinear field theory.Irena Rachůnková and Jan TomečekCopyright © 2010 Irena Rachůnková and Jan Tomeček. All rights reserved.http://www.hindawi.com/journals/bvp/2010/690342/For one-dimensional p-Laplacian with weights in ℒγ:=Lγ([0,1],ℝ)  (1≤γ≤∞) balls, we are interested in the extremal values of the mth positive half-eigenvalues associated with Dirichlet, Neumann, and generalized periodic boundary conditions, respectively. It will be shown that the extremal value problems for half-eigenvalues are equivalent to those for eigenvalues, and all these extremal values are given by some best Sobolev constants.Ping YanCopyright © 2010 Ping Yan. All rights reserved.