http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/103867.htmlThis paper studies the eigenvalue interval for the singular boundary value problem −u′′=g(t,u)+λh(t,u),   t∈(0,1),  u(0)=0=u(1), where g+h may be singular at u=0,  t=0,1, and may change sign and be superlinear at u=+∞. The approach is based on an approximation method together with the theory of upper and lower solutions.Haishen Lü, Ravi P. Agarwal, and Donal O'Regan© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/853607.htmlWe study stagnation zones of 𝒜-harmonic functions on canonical domains in the Euclidean n-dimensional space. Phragmén-Lindelöf type theorems are proved.Vladimir M. Miklyukov, Antti Rasila, and Matti Vuorinen© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/835865.htmlWe show some inequalities for generalized fractional integral operators on generalized Morrey spaces. We also show the boundedness property of the generalized fractional integral operators on the predual of the generalized Morrey spaces.Yoshihiro Sawano, Satoko Sugano, and Hitoshi Tanaka© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/584145.htmlBy using fixed point theorems in cones, the existence of multiple positive solutions is considered for nonlinear m-point boundary value problem for the following second-order boundary value problem on time scales (ϕ(uΔ))∇+a(t)f(t,u(t))=0, t∈(0,T), ϕ(uΔ(0))=∑i=1m−2aiϕ(uΔ(ξi)), u(T)=∑i=1m−2biu(ξi), where ϕ:R→R is an increasing homeomorphism and homomorphism and ϕ(0)=0. Some new results are obtained for the existence of twin or an arbitrary odd number of positive solutions of the above problem by applying Avery-Henderson and Leggett-Williams fixed point theorems, respectively. In particular, our criteria generalize and improve some known results by Ma and Castaneda (2001). We must point out for readers that there is only the p-Laplacian case for increasing homeomorphism and homomorphism. As an application, one example to demonstrate our results is given.Wei Han and Shugui Kang© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/135730.htmlThe goal of this paper is to establish the regularity of the solution of the first initial-boundary value problem for general higher-order hyperbolic equations in cylinders with the bases containing cuspidal points.Nguyen Manh Hung and Vu Trong Luong© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/185319.htmlThe nonlinear elliptic eigenvalue problem −div(|∇u|p−2∇u)−div(|∇u|q−2∇u)+λa(x)|u|p−2u+λb(x)|u|q−2u=f(x,u),u∈W1,p∩W1,q(RN), where 2≤q≤p<N and a(x)∈LN/p(RN),b(x)∈LN/q(RN),a(x),b(x)>0 are studied. The key ingredient is a special constrained minimization method.Mingzhu Wu and Zuodong Yang© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/191627.htmlThis paper investigates the existence and uniqueness of smooth positive solutions to a class of singular m-point boundary value problems of second-order ordinary differential equations. A necessary and sufficient condition for the existence and uniqueness of smooth positive solutions is given by constructing lower and upper solutions and with the maximal theorem. Our nonlinearity f(t,u,v) may be singular at v,t=0 and/or t=1.Xinsheng Du and Zengqin Zhao© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/654539.htmlA Holling type III predator-prey model with self- and cross-population pressure is considered. Using the energy estimate and Gagliardo-Nirenberg-type inequalities, the existence and uniform boundedness of global solutions to the model are dicussed. In addition, global asymptotic stability of the positive equilibrium point for the model is proved by Lyapunov function.Rui Zhang, Ling Guo, and Shengmao Fu© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/524846.htmlConsider the scattering of an electromagnetic time-harmonic plane wave by an infinite cylinder having an open crack Γ and a bounded domain D in R2 as cross section. We assume that the crack Γ is divided into two parts, and one of the two parts is (possibly) coated on one side by a material with surface impedance λ. Different boundary conditions are given on Γ and ∂D. Applying potential theory, the problem can be reformulated as a boundary integral system. We obtain the existence and uniqueness of a solution to the system by using Fredholm theory.Guozheng Yan© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/378763.htmlThis paper deals with a Holling type III diffusive predator-prey model with stage structure and nonlinear density restriction in the space ℝn. We first consider the asymptotical stability of equilibrium points for the model of ODE type. Then, the existence and uniform boundedness of global solutions and stability of the equilibrium points for the model of weakly coupled reaction-diffusion type are discussed. Finally, the global existence and the convergence of solutions for the model of cross-diffusion type are investigated when the space dimension is less than 6.Rui Zhang, Ling Guo, and Shengmao Fu© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/516390.htmlThis paper deals with the properties of positive solutions to a semilinear parabolic system with nonlocal boundary condition. We first give the criteria for finite time blowup or global existence, which shows the important influence of nonlocal boundary. And then we establish the precise blowup rate estimate for small weighted nonlocal boundary.Yulan Wang and Zhaoyin Xiang© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/137451.htmlA singular Cauchy-Nicoletti problem for a system of nonlinear ordinary differential equations is considered. With the aid of combination of Ważewski's topological method and Schauder's principle, the theorem concerning the existence of a solution of this problem (having the graph in a prescribed domain) is proved.Jaromír Baštinec, Josef Diblík, and Zdeněk Šmarda© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/572512.htmlWe consider the existence of countably many positive solutions for nonlinear nth-order three-point boundary value problem u(n)(t)+a(t)f(u(t))=0, t∈(0,1), u(0)=αu(η), u′(0)=⋯=u(n−2)(0)=0, u(1)=βu(η), where n≥2,α≥0,β≥0,0<η<1,α+(β−α)ηn−1<1, a(t)∈Lp[0,1] for some p≥1 and has countably many singularities in [0,1/2). The associated Green's function for the nth-order three-point boundary value problem is first given, and growth conditions are imposed on nonlinearity f which yield the existence of countably many positive solutions by using the Krasnosel'skii fixed point theorem and Leggett-Williams fixed point theorem for operators on a cone.Yude Ji and Yanping Guo© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/393259.htmlA new fixed point theorem in a cone is applied to obtain the existence of positive solutions of some fourth-order beam equation boundary value problems with dependence on the first-order derivative u(iυ)(t)=f(t,u(t),u′(t)),0<t<1,u(0)=u(1)=u′′(0)=u′′(1)=0, where f:[0,1]×[0,∞)×R→[0,∞) is continuous.Jinhui Liu and Weiya Xu© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/708389.htmlWe investigate the existence of weak solutions to the following Dirichlet boundary value problem, which occurs when modeling an injection molding process with a partial slip condition on the boundary. We have −Δθ=k(θ)|∇p|r+q(x) in Ω; −div{(k(θ)|∇p|r−2+β(x)|∇p|r0−2)∇p}=0 in Ω; θ=θ0, and p=p0 on ∂Ω.Ming Fang and Robert P. Gilbert© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/316812.htmlWe study the existence and multiplicity of classical solutions for second-order impulsive Sturm-Liouville equation with Neumann boundary conditions. By using the variational method and critical point theory, we give some new criteria to guarantee that the impulsive problem has at least one solution, two solutions, and infinitely many solutions under some different conditions, respectively. Some examples are also given in this paper to illustrate the main results.Juntao Sun and Haibo Chen© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/845946.htmlWe establish new results concerning existence and asymptotic behavior of entire, positive, and bounded solutions which converge to zero at infinite for the quasilinear equation −Δpu=a(x)f(u)+λb(x)g(u),  x∈ℝN,  1<p<N, where f,g:[0,∞)→[0,∞) are suitable functions and a(x),b(x)≥0 are not identically zero continuous functions. We show that there exists at least one solution for the above-mentioned problem for each 0≤λ<λ⋆, for some λ⋆>0. Penalty arguments, variational principles, lower-upper solutions, and an approximation procedure will be explored.C. A. Santos© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/563767.htmlWe study the long-time behavior of solution for the m-Laplacian equation ut−div(|∇u|m−2∇u)+λ|u|m−2u+f(x,u)=g(x) in RN×R+, in which the nonlinear term f(x,u) is a function like f(x,u)=−h(x)|u|q−2u with h(x)≥0, 2≤q<m, or f(x,u)=a(x)|u|α−2u−h(x)|u|β−2u with a(x)≥h(x)≥0 and α>β≥m. We prove the existence of a global (L2(RN),Lp(RN))-attractor for any p>m.Caisheng Chen, Lanfang Shi, and Hui Wang© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/691496.htmlThe initial boundary value problem for a nonlinear hyperbolic equation with Lewis function in a bounded domain is considered. In this work, the main result is that the solution blows up in finite time if the initial data possesses suitable positive energy. Moreover, the estimates of the lifespan of solutions are also given.Faramarz Tahamtani© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/959636.htmlThis paper investigates the singular differential equation (p(t)u′)′=p(t)f(u), having a singularity at t=0. The existence of a strictly increasing solution (a homoclinic solution) satisfying u′(0)=0, u(∞)=L>0 is proved provided that f has two zeros and a linear behaviour near −∞.Irena Rachůnková and Jan Tomeček© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/710386.htmlSufficient coefficient conditions for the correct and unique solvability of the boundary-value problem for one class of operator-differential equations of the fourth order with complex characteristics, which cover the equations arising in solving the problems of stability of plastic plates, are obtained in this paper. Exact values of the norms of operators of intermediate derivatives, which are involved in the perturbed part of the operator-differential equation under investigation, are found along with these in subspaces W24(R+;H) in relation to the norms of the operator generated by the main part of this equation. It is noted that this problem has its own mathematical interest.Araz R. Aliev and Aydin A. Gasymov© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/896813.htmlWe focus in this paper on the theoretical and numerical aspect os image processing. We consider a non linear boundary value problem (the p-Laplacian) from which we will derive the asymptotic expansion of the Mumford-Shah functional. We give a theoretical expression of the topological gradient as well as a numerical confirmation of the result in the restoration and segmentation of images.Alassane Sy and Diaraf Seck© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/156063.htmlUsing Mountain Pass Lemma, we obtain the existence of nontrivial weak solutions for a class of superlinear and nonhomogeneous quasilinear equations. The key factor in this paper is to use the new idea of near p-homogeneity in conjunction with variational techniques to obtain a new multiplicity result for a vast set of nonlinear equations, such as the mean curvature equation and so on.Gao Jia, Qing Zhao, and Chun-yan Dai© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/685040.htmlWe are concerned with the following nonlinear second-order three-point boundary value problem on time scales −xΔΔ(t)=f(t,x(t)), t∈[a,b]𝕋, x(a)=0, x(σ2(b))=δx(η), where a,b∈𝕋 with a<b,    η∈(a,b)𝕋 and 0<δ<(σ2(b)−a)/(η−a). A new representation of Green's function for the corresponding linear boundary value problem is obtained and some existence criteria of at least one positive solution for the above nonlinear boundary value problem are established by using the iterative method.Jian-Ping Sun© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/127510.htmlBy employing the contraction mapping principle and applying Gronwall-Bellman's inequality, sufficient conditions are established to prove the existence and exponential stability of positive almost periodic solution for nonlinear impulsive delay model of hematopoiesis.J. O. Alzabut, J. J. Nieto, and G. Tr. Stamov© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/362983.htmlWe are concerned with the higher-order nonlinear three-point boundary value problems: x(n)=f(t,x,x′,…,x(n−1)),n≥3, with the three point boundary conditions g(x(a),x′(a),…,x(n−1)(a))=0; x(i)(b)=μi,i=0,1,…,n−3;h(x(c),x′(c),…,x(n−1)(c))=0, where a<b<c,f:[a,c]×ℝn→ℝ=(−∞,+∞) is continuous, g,h:ℝn→ℝ are continuous, and μi∈ℝ,i=0,1,…,n−3 are arbitrary given constants. The existence and uniqueness results are obtained by using the method of upper and lower solutions together with Leray-Schauder degree theory. We give two examples to demonstrate our result.Minghe Pei and Sung Kag Chang© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/873526.htmlWe generalize the comparison result 2007 on Hamilton-Jacobi equations to nonlinear parabolic equations, then by using Perron's method to study the existence and uniqueness of time almost periodic viscosity solutions of nonlinear parabolic equations under usual hypotheses.Shilin Zhang and Daxiong Piao© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/287834.htmlThis paper deals with a two-point boundary value problem of a class of Duffing-type systems with non-C1 perturbation term. Several existence and uniqueness theorems were presented.Jiang Zhengxian and Huang Wenhua© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/937064.htmlWe are concerned with singular three-point boundary value problems for delay higher-order dynamic equations on time scales. Theorems on the existence of positive solutions are obtained by utilizing the fixed point theorem of cone expansion and compression type. An example is given to illustrate our main result.Liang-Gen Hu, Ti-Jun Xiao, and Jin Liang© 2010, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/bvp/2009/634324.htmlThe existence of a step-like contrast structure for a class of high-dimensional singularly perturbed system is shown by a smooth connection method based on the existence of a first integral for an associated system. In the framework of this paper, we not only give the conditions under which there exists an internal transition layer but also determine where an internal transition time is. Meanwhile, the uniformly valid asymptotic expansion of a solution with a step-like contrast structure is presented.Mingkang Ni and Zhiming Wang© 2010, Hindawi Publishing Corporation. All rights reserved.