http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/860414This paper deals with the existence and iteration of positive solutions for the following one-dimensional p-Laplacian boundary value problems: (ϕp(u′(t)))′+a(t)f(t,u(t),u′(t))=0, t∈(0,1), subject to some boundary conditions. By making use of monotone iterative technique, not only we obtain the existence of positive solutions for the problems, but also we establish iterative schemes for approximating the solutions.Zhiyong Wang and Jihui Zhang© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/728603The existence of at least three positive solutions for differential equation (ϕp(u′(t)))′+g(t)f(t,u(t),u′(t))=0, under one of the following boundary conditions: u(0)=∑i=1m−2aiu(ξi), φp(u′(1))=∑i=1m−2biφp(u′(ξi)) or φp(u′(0))=∑i=1m−2aiφp(u′(ξi)), u(1)=∑i=1m−2biu(ξi) is obtained by using the H. Amann fixed point theorem, where φp(s)=|s|p−2s, p>1, 0<ξ1<ξ2<⋯<ξm−2<1, ai>0, bi>0, 0<∑i=1m−2ai<1, 0<∑i=1m−2bi<1. The interesting thing is that g(t) may be singular at any point of [0,1] and f may be noncontinuous.Weihua Jiang, Bin Wang, and Yanping Guo© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/847145We study the global existence and the global nonexistence of a non-Newtonian polytropic filtration system coupled via nonlinear boundary flux. We first establish a weak comparison principle, then discuss the large time behavior of solutions by using modified upper and lower solution methods and constructing various upper and lower solutions. Necessary and sufficient conditions on the global existence of all positive (weak) solutions are obtained.Zhongping Li, Chunlai Mu, and Yuhuan Li© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/859461This paper deals with a boundary value problem for Duffing equation. The existence of unique solution for the problem is studied by using the minimax theorem due to Huang Wenhua. The existence and uniqueness result was presented under a generalized nonresonance condition.Zhou Ting and Huang Wenhua© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/395080We find the second positive radial solution for the following p-Laplacian problem: div(|∇u|p−2∇u)+K(|x|)uq=0 in Ω, u|∂Ω=0, u(x)→μ>0 as |x|→∞, where Ω={x∈ℝN:|x|>r0}, r0>0, N>p>1, K∈C(Ω,(0,∞)) and q>p−1. We also give some global existence results with respect to the parameter μ.Chan-Gyun Kim, Yong-Hoon Lee, and Inbo Sim© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/217636We obtain the existence of a nontrivial solution for a class of subcritical elliptic systems with indefinite weights in R2. The proofs base on Trudinger-Moser inequality and a generalized linking theorem introduced by Kryszewski and Szulkin.Guoqing Zhang and Sanyang Liu© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/814947This paper is devoted to the study of a mixed problem for a nonlinear parabolic integro-differential equation which mainly arise from a one dimensional quasistatic contact problem. We prove the existence and uniqueness of solutions in a weighted Sobolev space. Proofs are based on some a priori estimates and on the Schauder fixed point theorem. we also give a result which helps to establish the regularity of a solution.Said Mesloub© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/194234In this paper, We study the existence and uniqueness of solutions for boundary value problems to the singular one-dimension p-Laplacian by using mixed monotone method. Our results improve several recent results established in the literature.Xiaoning Lin, Weizhi Sun, and Daqing Jiang© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/749865Solving an inverse Sturm-Liouville problem requires a mathematical process to determine unknown function in the Sturm-Liouville operator from given data in addition to the boundary values. In this paper, we identify a Sturm-Liouville potential function by using the data of one eigenfunction and its corresponding eigenvalue, and identify a spatial-dependent unknown function of a Sturm-Liouville differential operator. The method we employ is to transform the inverse Sturm-Liouville problem into a parameter identification problem of a heat conduction equation. Then a Lie-group estimation method is developed to estimate the coefficients in a system of ordinary differential equations discretized from the heat conduction equation. Numerical tests confirm the accuracy and efficiency of present approach. Definite and random disturbances are also considered when comparing the present method with that by using a technique of numerical differentiation.Chein-Shan Liu© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/831746We consider the attractors for the two-dimensional nonautonomous Navier-Stokes equations in some unbounded domain Ω with nonhomogeneous boundary conditions. We apply the so-called uniformly ω-limit compact approach to nonhomogeneous Navier-Stokes equation as well as a method to verify it. Assuming f∈Lloc2((0,T);L2(Ω)), which is translation compact and φ∈Cb1(ℝ+;H2(ℝ1×{±L})) asymptotically almost periodic, we establish the existence of the uniform attractor in H1(Ω).Delin Wu© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/723828Using the theory of coincidence degree, we establish existence results of positive solutions for higher-order multi-point boundary value problems at resonance for ordinary differential equation u(n)(t)=f(t,u(t),u′(t),…,u(n−1)(t))+e(t),    t∈(0,1), with one of the following boundary conditions: u(i)(0)=0, i=1,2,…, n−2, u(n−1)(0)=u(n−1)(ξ), u(n−2)(1)=∑j=1m−2βju(n−2)(ηj), and u(i)(0)=0, i=1,2,…, n−1, u(n−2)(1)=∑j=1m−2βju(n−2)(ηj), where f:[0,1]×ℝn→ℝ=(−∞,+∞) is a continuous function, e(t)∈L1[0,1]βj∈ℝ (1≤j≤m−2, m≥4), 0<η1<η2<⋯<ηm−2<1, 0<ξ<1, all the β−j−s have not the same sign. We also give some examples to demonstrate our results.Yunzhu Gao and Minghe Pei© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/123823By mixed monotone method, the existence and uniqueness are established for singular higher-order continuous and discrete boundary value problems. The theorems obtained are very general and complement previous known results.Chengjun Yuan, Daqing Jiang, and You Zhang© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/389028For higher-order functional differential equations and, particularly, for nonautonomous differential equations with deviated arguments, new sufficient conditions for the existence and uniqueness of a periodic solution are established.I. Kiguradze, N. Partsvania, and B. Půža© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/293987We show the existence of four 2π-periodic solutions of the nonlinear Hamiltonian system with some conditions. We prove this problem by investigating the geometry of the sublevels of the functional and two pairs of sphere-torus variational linking inequalities of the functional and applying the critical point theory induced from the limit relative category.Tacksun Jung and Q-Heung Choi© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/735846This paper is concerned with an initial boundary value problem in one-dimensional magnetohydrodynamics. We prove the global existence, uniqueness, and stability of strong solutions for the planar magnetohydrodynamic equations for isentropic compressible fluids in the case that vacuum can be allowed initially.Jianwen Zhang© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/254593We consider the nonlinear eigenvalue problems u″+rf(u)=0, 0<t<1, u(0)=0, u(1)=∑i=1m−2αiu(ηi), where m≥3, ηi∈(0,1), and αi>0 for i=1,…,m−2, with ∑i=1m−2αi<1; r∈ℝ; f∈C1(ℝ,ℝ). There exist two constants s2<0<s1 such that f(s1)=f(s2)=f(0)=0 and f0:=limu→0(f(u)/u)∈(0,∞), f∞:=lim|u|→∞(f(u)/u)∈(0,∞). Using the global bifurcation techniques, we study the global behavior of the components of nodal solutions of the above problems.Yulian An and Ruyun Ma© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/574842We establish the existence of multiple positive solutions for a singular nonlinear third-order periodic boundary value problem. We are mainly interested in the semipositone case. The proof relies on a nonlinear alternative principle of Leray-Schauder, together with a truncation technique.Yigang Sun© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/385874We study the problem of finding a Hermitian monogenic function with a given jump on a given hypersurface in ℝm, m=2n. Necessary and sufficient conditions for the solvability of this problem are obtained.Ricardo Abreu Blaya, Juan Bory Reyes, Dixan Peña Peña, and Frank Sommen© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/236386We study existence of positive solutions of the nonlinear system −(p1(t,u,v)u′)′= h1(t)f1(t,u,v) in (0,1); −(p2(t,u,v)v′)′=h2(t)f2(t,u,v) in (0,1); u(0)=u(1)=v(0)=v(1)=0, where p1(t,u,v)=1/(a1(t)+c1g1(u,v)) and p2(t,u,v)=1/(a2(t)+c2g2(u,v)). Here, it is assumed that g1, g2 are nonnegative continuous functions, a1(t), a2(t) are positive continuous functions, c1,c2≥0, h1,h2∈L1(0,1), and that the nonlinearities f1, f2 satisfy superlinear hypotheses at zero and +∞. The existence of solutions will be obtained using a combination among the method of truncation, a priori bounded and Krasnosel'skii well-known result on fixed point indices in cones. The main contribution here is that we provide a treatment to the above system considering differential operators with nonlinear coefficients. Observe that these coefficients may not necessarily be bounded from below by a positive bound which is independent of u and v.Patricio Cerda and Pedro Ubilla© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/27621The solvability for a class of abstract two-point boundary value problems derived from optimal control is discussed. By homotopy technique existence and uniqueness results are established under some monotonic conditions. Several examples are given to illustrate the application of the obtained results.Lianwen Wang© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/68758We are concerned with the nonlinear fourth-order three-point boundary value problem u(4)(t)=a(t)f(u(t)), 0<t<1, u(0)=u(1)=0, αu″(η)−βu‴(η)=0, γu″(1)+δu‴(1)=0. By using Krasnoselskii's fixed point theorem in a cone, we get some existence results of positive solutions.Chuanzhi Bai© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/17951Using fixed point index theory, we obtain several sufficient conditions of existence of at least one positive solution for third-order m-point boundary value problems.Weihua Jiang and Fachao Li© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/85621Using variational methods, we prove the existence and nonexistence of positive solutions for a class of (p,q)-Laplacian systems with a parameter.Said El Manouni and Kanishka Perera© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/18961The paper discusses the existence of positive solutions, dead core solutions, and pseudo dead core solutions of the singular problem (φ(u′))′+f(t,u′)=λg(t,u,u′), u′(0)=0, βu′(T)+αu(T)=A. Here λ is a positive parameter, β≥0, α, A>0, f may be singular at t=0 and g is singular at u=0.Ravi P. Agarwal, Donal O'Regan, and Svatoslav Staněk© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/64012In a recent paper, Sun et al. (2007) studied the existence of positive solutions of nonhomogeneous multipoint boundary value problems for a second-order differential equation. It is the purpose of this paper to show that the shooting method approach proposed in the recent paper by the first author can be extended to treat this more general problem.Man Kam Kwong and James S. W. Wong© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/97067By Leray-Schauder continuation theorem and the nonlinear alternative of Leray-Schauder type, the existence of a solution for an m-point boundary value problem with impulses is proved.Jianli Li and Sanhui Liu© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/56945This work is concerned with the relaxation-time limit of the multidimensional isothermal Euler equations with relaxation. We show that Coulombel-Goudon's results (2007) can hold in the weaker and more general Sobolev space of fractional order. The method of proof used is the Littlewood-Paley decomposition.Jiang Xu and Daoyuan Fang© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/23108Krasnoselskii's fixed-point theorem in a cone is used to discuss the existence of positive solutions to semipositone right focal eigenvalue problems (−1)n−pu(n)(t)=λf(t,u(t),u'(t),…,u(p−1)(t)), u(i)(0)=0, 0≤i≤p−1, u(i)(1)=0, p≤i≤n−1, where n≥2, 1≤p≤n−1 is fixed, f:[0,1]×[0,∞)p→(−∞,∞) is continuous with f(t,u1,u2,…,up)≥−M for some positive constant M.Yuguo Lin and Minghe Pei© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/38230The existence of positive solutions for boundary value problems of nonlinear functional difference equations with p-Laplacian operator is investigated. Sufficient conditions are obtained for the existence of at least one positive solution and two positive solutions.S. J. Yang, B. Shi, and D. C. Zhang© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/42954We construct for every fixed n≥2 the metric gs=h1(r)dt2−h2(r)dr2−k1(ω)dω12−⋯−kn−1(ω)dωn−12, where h1(r), h2(r), ki(ω), 1≤i≤n−1, are continuous functions, r=|x|, for which we consider the Cauchy problem (utt−Δu)gs=f(u)+g(|x|), where x∈ℝn, n≥2; u(1,x)=u∘(x)∈L2(ℝn), ut(1,x)=u1(x)∈H˙−1(ℝn), where f∈𝒞1(ℝ1), f(0)=0, a|u|≤f′(u)≤b|u|, g∈𝒞(ℝ+), g(r)≥0, r=|x|, a and b are positive constants. When g(r)≡0, we prove that the above Cauchy problem has a nontrivial solution u(t,r) in the form u(t,r)=v(t)ω(r) for which limt→0‖u‖L2([0,∞))=∞. When g(r)≠0, we prove that the above Cauchy problem has a nontrivial solution u(t,r) in the form u(t,r)=v(t)ω(r) for which limt→0‖u‖L2([0,∞))=∞.Svetlin Georgiev Georgiev© 2008, Hindawi Publishing Corporation. All rights reserved.