Three solutions for a p-Laplacian boundary value problem with impulsive effects

In this paper, a p-Laplacian boundary value problem with impulsive effects is considered. Multiplicity of solutions is obtained by three critical points theorem. An example is presented to illustrate main result.     

Three solutions for a mixed boundary value problem involving the one-dimensional p-Laplacian

This paper deals with two mixed nonlinear boundary value problems depending on a parameter λ. For each of them we prove the existence of at least three generalized solutions when λ lies in an exactly determined open interval. Usefulness of this information on the interval is then emphasized by means of some consequences. Our main tool is a very recent three critical points theorem stated in [Topol. Methods Nonlinear Anal. 22 (2003) 93-104].     

Positive solutions for a fractional boundary value problem with p-Laplacian operator

In this paper, we are mainly concerned with positive solutions for a p-Laplacian fractional boundary value problem. By virtue of Jensen’s inequalities and some new properties of the Green function of the problem, we adopt the Krasnoselskii-Zabreiko fixed point theorem to establish the results of existence and multiplicity of the positive solutions. Finally, a uniqueness theorem is established by using a fixed point theorem of concave operator and an example is given to illustrate the result.     

The second initial boundary value problem for the gravitation-gyroscopic wave equation in exterior domains

We study the existence and uniqueness of the solution to the second initial boundary value problem for the gravitation-gyroscopic wave equation in an exterior multiply connected domain with various types of conditions at infinity. Translated fromMatematicheskie Zametki, Vol. 60, No. 1, pp. 40–57, July, 1996. This research was partially supported by the Russian Foundation for Basic Research under grant No. 96-01-01411.     

Infinitely many solutions for a p-Laplacian boundary value problem with impulsive effects

In this paper, a p-Laplacian boundary value problem with impulsive effects is considered. By using variational methods and critical point theorems, some criteria are obtained to guarantee that the impulsive problem has infinitely many solutions when the impulsive functions satisfy superlinear or sublinear conditions. Our results further improve some existing results.     

Regularity of solutions to Dirichlet boundary value problem in domains on a manifold

The regularity of solutions to the Dirichlet boundary value problem is studied for elliptic differential operators of order 2m defined on subdomains of a manifold. Relationships between the smoothness of the right hand side, the boundary, and the solutions are obtained.     

带p-Laplacian算子三点边值问题拟对称正解的多重性

应用Avery—Peterson不动点定理,讨论了一类带p-Laplacian算子三点边值问题在非线性项,依赖于未知函数的一阶导数的情况下拟对称正解的多重性,得到了这类边值问题至少存在三个拟对称正解的充分条件．     

具p-Laplace算子的分数阶微分方程边值问题的正解

考虑具有p-Laplace算子的分数阶泛函微分方程边值问题,利用锥上的不动点定理,得到了其正解及多个正解存在的充分条件,所得结果推广了已有的结论,并举例说明了结论的适用性.     

Positive solutions for a p-Laplacian type system of impulsive fractional boundary value problem

In this paper, the aim is to discuss a class of p-Laplacian type fractional Dirichlet"s boundary value problem involving impulsive impacts. Based on the approaches of variational method and the properties of fractional derivatives on the reflexive Banach spaces, the existence results of positive solutions for our equations are established. Two examples are given at the end of each main result.     

On solutions of the mixed Dirichlet-Steklov problem for the biharmonic equation in exterior domains

We study the unique solvability of the mixed Dirichlet-Steklov problem for the biharmonic equation in exterior domains under the assumption that a generalized solution of this problem has a bounded Dirichlet integral with weight |x| ^a . Depending on the value of the parameter a, we prove uniqueness theorem or present exact formulas for the dimension of the solution space of the mixed Dirichlet-Steklov problem in the exterior of a compact set.     

An exterior boundary value problem in Minkowski space

In three‐dimensional Lorentz–Minkowski space ??³, we consider a spacelike plane Π and a round disc Ω over Π. In this article we seek the shapes of unbounded surfaces whose boundary is ? Ω and its mean curvature is a linear function of the distance to Π. These surfaces, called stationary surfaces, are solutions of a variational problem and governed by the Young–Laplace equation. In this sense, they generalize the surfaces with constant mean curvature in ??³. We shall describe all axially symmetric unbounded stationary surfaces with special attention in the case that the surface is asymptotic to Π at the infinity. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Existence of positive solutions for Sturm-Liouville-like boundary value problem with p-Laplacian on time scales

We consider the existence of positive solutions for a class of Sturm-Liouville-like boundary value problem with p-Laplacian on time scales. Using the well known Krasnosel’ski’s fixed point theorem, some new existence criteria for positive solutions of the boundary value problem are presented. As an application, two examples are given to illustrate the main results.     

On the existence of nonnegative solutions to the Dirichlet boundary value problem for the p-Laplace equation in the presence of exterior mass forces

We consider the Dirichlet problem for an inhomogeneous p-Laplace equation with nonlinear source in the presence of exterior mass forces.We obtain new sufficient conditions for the existence of a weak nonnegative bounded solution. The sufficient conditions are written in explicit form through the data of the problem.     

A class of explicit solutions for the Soret-Dufour boundary value problem in arbitrary domains

A method is proposed for finding explicit solutions to the Soret-Dufour boundary value problem. This is done solving a two-point problem for a system of ordinary differential equations of the first order.     

On the number of bounded positive solutions of the exterior elliptic boundary value problems

Positive linear functionals on a ¹-algebra are studied. The first purpose of this paper is to investigate the classification of semibounded abelian positive linear functionals. The second purpose is to study the integral representation of positive linear functionals.