Positive Solutions of a Class of Quasilinear Elliptic Equations in Two-dimensional Exterior Domains

Sufficient conditions for the existence of positive solutions to a class of quasilinear elliptic equations in two-dimensional exterior domains are given.     

具奇异边界条件的一类拟线性椭圆型方程

得到了一类拟线性椭圆型方程爆破解的存在性。     

Morrey global bounds and quasilinear Riccati type equations below the natural exponent

We obtain global bounds in Lorentz–Morrey spaces for gradients of solutions to a class of quasilinear elliptic equations with low integrability data. The results are then applied to obtain sharp existence results in the framework of Morrey spaces for Riccati type equations with a gradient source term having growths below the natural exponent of the operator involved. A special feature of our results is that they hold under a very general assumption on the nonlinear structure, and under a mild natural restriction on the boundary of the ground domain.     

Global solutions for quasilinear parabolic problems

Results on the global existence of classical solutions for quasilinear parabolic equations in bounded domains with homogeneous Dirichlet or Neumann boundary conditions are presented. Besides quasilinear parabolic equations, the method is also applicable to some weakly-coupled reaction-diffusion systems and to elliptic equations with nonlinear dynamic boundary conditions. Received December 21, 2000; accepted August 30, 2001.     

The method of upper and lower solutions for diffraction problems of quasilinear elliptic reaction-diffusion systems

The aim of this paper is to show the existence of solutions of the n-dimensional diffraction problem for weakly coupled quasilinear elliptic reaction-diffusion system. The coefficients of the equations under consideration are allowed to be discontinuous. We extend the method of upper and lower solutions for reaction-diffusion equations with continuous coefficients to the elliptic diffraction problem. An application of these results is given to the steady-state problem of Lotka-Volterra cooperation model with two cooperating species.     

NONRADIAL POSITIVE SOLUTIONS TO SINGULAR QUASILINEAR ELLIPTIC EQUATIONS IN THE PLANE

This paper investigates 2-dimensional singular,quasilinear elliptic equations and gives some suffcient conditions ensuring the equations have infinitely many positive entire solutions. The super-subsolution method is used to prove the existence of such solutions.     

Two types of quasilinear elliptic equations with degenerate coerciveness and slightly superlinear growth

The existence of positive solutions for two types of quasilinear elliptic equations with degenerate coerciveness and slightly superlinear growth is established. Especially, we solve an open problem proposed in the literature (Mercaldo and Peral, 2008).     

在无界区域上拟线性散度型椭圆型方程的Dirichlet问题

研究在无界区域上的二阶拟线性散度型椭圆型方程Dirichlet问题在无穷远处径向收敛的古典解存在性和唯一性。     

Positive solutions for critical quasilinear elliptic equations with mixed dirichlet-neumann boundary conditions

The existence and multiplicity of positive solutions are studied for a class of quasilinear elliptic equations involving Sobolev critical exponents with mixed Dirichlet-Neumann boundary conditions by the variational methods and some analytical techniques.     

A concentration-compactness principle at infinity and positive solutions of some quasilinear elliptic equations in unbounded domains

In this paper, we formulate a concentration-compactness principle at infinity which extends a result introduced by J. Chabrowski [Calc. Var. Partial Differential Equations 3 (1995) 493-512]. Then we consider some quasilinear elliptic equations in some classes of unbounded domains by solving their corresponding constrained minimization problems under certain conditions. We show the existence of positive solutions of those equations via the concentration-compactness principle at infinity, which extends some results in [Differential Integral Equations 6 (1993) 1281-1298].     

Multiple Sign-Changing Solutions for Quasilinear Equations of Bounded Quasilinearity

The existence of an infinite sequence of sign-changing solutions are proved for a class of quasilinear elliptic equations under suitable conditions on the quasilinear coefficients and the nonlinearity■ where ? ? R~N is a bounded domain with smooth boundary, and we use■ The main interest of this paper is for the case of bounded quasilinearity bij. The result is proved by an elliptic regularization method involving truncations of both u and the gradient of u.     

Existence and Uniqueness of Positive Radial Solutions for a Class of Quasilinear Elliptic Systems

This article is concerned with the existence and uniqueness of positive radial solutions for a class of quasilinear elliptic system. With some reasonable assumptions on the nonlinear source functions and their coefficients, the existence and the upper and lower bounds of the positive solutions will be provided by using the fixed point theorem and the maximum principle for the quasilinear elliptic system.     

Enclosure results for quasilinear systems of variational inequalities

In this paper we consider systems of quasilinear elliptic variational inequalities, and prove the existence of minimal and maximal (in the set theoretical sense) solutions within some ordered interval of an appropriately defined pair of sub- and supersolutions. We show that the notion of sub- and supersolutions of variational inequalities introduced here is consistent with the usual notion of sub-supersolutions for (variational) equations. For weakly coupled quasimonotone systems of variational inequalities the existence of smallest and greatest solutions is proved.     

双退化拟线性椭圆型方程Keldys-Fichera障碍问题

讨论一类双退化散度型拟线性椭圆型方程的Keldys-Fichera障碍问题,证明了解的存在性.     

Existence of three solutions for quasilinear elliptic equations: an Orlicz-Sobolev space setting

In this paper, we establish the existence of three weak solutions for quasilinear elliptic equations in an Orlicz-Sobolev space via an abstract result recently obtained by Ricceri in [13].     

Existence and uniqueness of solutions for quasilinear elliptic systems

We obtain necessary and sufficient conditions for the existence of positive solutions for a class of sublinear Dirichlet quasilinear elliptic systems.

     

Quasilinear elliptic equations on $$\mathbb{R}^N $$with infinitely many solutions

We give verifiable conditions ensuring that second order quasilinear elliptic equations on have infinitely many solutions in the Sobolev space for generic right-hand sides. This amounts to translating in concrete terms the more elusive hypotheses of an abstract theorem. Salient points include the proof that a key denseness property is equivalent to the existence of nontrivial solutions to an auxiliary problem, and an estimate of the size of the set of critical points of nonlinear Schrödinger operators. Conditions for the real-analyticity of Nemytskii operators are also discussed.     

具有梯度项的Schrdinger型拟线性椭圆型方程组的全空间解的存在性

研究了全空间下的具有梯度项的Schrdinger型拟线性椭圆型方程组的解的存在性.     

一阶椭圆型复方程组Riemann－Hilbert边值问题

本文以解析函数的边值问题Ｂ的解的存在性为基础，根据它们的先验估计式及利用参数开拓法，导出了满足条件Ｃ的多个复变量的一阶拟线性椭圆型复方程组的Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ边值问题的可解条件，并给出了解的积分表达式．     

一类拟线性椭圆型方程组的正对称解的存在性

本文讨论了球域上一类拟线性椭圆型方程组正对称解的存在性和多解性