On some nonlinear elliptic systems

Abstract

The aim of this paper is to show that Liouville type property is a sufficient and necessary condition for the regularity of weak solutions of nonlinear elliptic systems of the higher order.

Nonexistence Of Result For Some P-laplacian Systems

“…In the case when p = 2,system (2) studied by Dalmasso [4]. For existence results of positive solutions for (2) see [2,3,5]. For corresponding results in the single equations case, see [1] for (1) and [6] for (2).…”

A Remark On Positive Solution For A Class Of P,q-laplacian Nonlinear System With Sign-changing Weight And Combined Nonlinear Effects

“…However, due to the loss of the variational structure, the treatment of nonvariational systems like (1) is more complicated and is based mostly on topological methods [15]. We refer to [16], [17], [18], [19] for additional results on elliptic problems involving the p-Laplacian.…”

Existence of Weak Solution for Nonlinear Elliptic Systems

“…In recent years,many publications have appeared concerning quasilinear elliptic systems which have been used in a great variety of applications,we refer the readers to [5,6,7,8,9] used variational methods to obtain weak solution of semlinear elliptic system and quasilinear elliptic system.…”