Weak solvability of nonlinear elliptic equations involving variable exponents

ON QUASILINEAR ELLIPTIC SYSTEMS INVOLVING MULTIPLE CRITICAL EXPONENTS

In this paper, we consider the existence of a non-trivial weaksolution to a quasilinear elliptic system involving critical Hardyexponents. The main issue of the paper is to understand thebehavior of these Palais-Smale sequences. Indeed, the principaldifficulty here is that there is an asymptotic competition betweenthe energy functional carried by the critical nonlinearities. Thenby the variatio...

Nonexistence results for a class of nonlinear elliptic equations involving critical Sobolev exponents

Solvability of nonlinear elliptic equations with gradient terms

We study the solvability in the whole Euclidean space of coercive quasi-linear and fully nonlinear elliptic equations modeled on ∆u±g(|∇u|) = f(u), u ≥ 0, where f and g are increasing continuous functions. We give conditions on f and g which guarantee the availability or the absence of positive solutions of such equations in R . Our results considerably improve the existing ones and are sharp o...

The Dirichlet Problems for Nonlinear Elliptic Equations with Variable Exponents on Riemannian Manifolds∗

In this paper, after discussing the properties of the Nemytsky operator, we obtain the existence of weak solutions for Dirichlet problemss of non-homogeneous p(m)-harmonic equations.

A Comparison Result and Elliptic Equations Involving Subcritical Exponents Nonlinear Diiusion Equations and Their Equilibrium States 3

It is well known that good bounds for solutions of nonlinear diierential equations are diicult to obtain. In this paper, we establish a theorem comparing non-negative solutions (having identical initial values) of the equations u 00 (t) + q(t)u p (t) + r(t)u(t) = 0 and v 00 (t) + k(t)q(t)v p (t) + r(t)u(t) = 0, respectively. If q(t); r(t) 0, k(t) 1, k(t) is non-decreasing, and the rst equation ...