http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/864297We 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/GetArticle.aspx?doi=10.1155/2008/425256We 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/GetArticle.aspx?doi=10.1155/2008/937138This 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/GetArticle.aspx?doi=10.1155/2008/403761Existence 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/GetArticle.aspx?doi=10.1155/2008/457028Positive 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/GetArticle.aspx?doi=10.1155/2008/197205Some 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/GetArticle.aspx?doi=10.1155/2008/752827This 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/GetArticle.aspx?doi=10.1155/2008/901503This 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.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/320603This paper is concerned with nonhomogeneous multipoint boundary value problems of second-order differential equations with one-dimensional p-Laplacian. Sufficient conditions to guarantee the existence of at least three solutions (may be not positive) of these BVPs are established.Xingyuan Liu© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/628973We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and the quasiperiodic boundary conditions. Using these asymptotic formulas, we find conditions on the coefficients for which the root functions of this operator form a Riesz basis. Then, we obtain the uniformly convergent spectral expansion of the differential operators with the periodic matrix coefficients.O. A. Veliev© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/963753The study in this paper is a numerical integration of second-order three-point boundary value problems under two imposed nonlocal boundary conditions at t=t0, t=ξ, and t=t1 in a general setting, where t0<ξ<t1. We construct a two-stage Lie-group shooting method for finding unknown initial conditions, which are obtained through an iterative solution of derived algebraic equations in terms of a weighting factor r∈(0,1). The best r is selected by matching the target with a minimal discrepancy. Numerical examples are examined to confirm that the new approach has high efficiency and accuracy with a fast speed of convergence. Even for multiple solutions, the present method is also effective to find them.Chein-Shan Liu© 2009, 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© 2009, 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© 2009, 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© 2009, 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© 2009, 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© 2009, 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© 2009, 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© 2009, 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© 2009, 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© 2009, 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© 2009, 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© 2009, 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© 2009, 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© 2009, 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© 2009, 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© 2009, 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© 2009, 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© 2009, 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© 2009, 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© 2009, Hindawi Publishing Corporation. All rights reserved.