The aim of this paper is to study the existence of solutions for a quasilinear elliptic system where the nonlinear term is a Caratheodory function on a bounded domain of R , by proving the well known unique continuation property for elliptic system in all dimensions: 1, 2, 3, . . . and the strict monotonocity of eigensurfaces. These properties let us to consider the above problem as a nonresona...

Let Ω 0 be an-open bounded domain in R N ≥ 3 and p∗ pN/ N − p . We consider the following quasilinear elliptic system of two equations inW 0 Ω ×W 1,p 0 Ω : −Δpu λf x |u|q−2u α/ α β h x |u|α−2u|v|β,−Δpv μg x |v|q−2v β/ α β h x |u|α|v|β−2v, where λ, μ > 0, Δp denotes the p-Laplacian operator, 1 ≤ q < p < N,α, β > 1 satisfy p < α β ≤ p∗, and f, g, h are continuous functions on Ω which are somewher...

The prior estimate and decay property of positive solutions are derived for a system of quasilinear elliptic 9 di$erential equations 3rst. Then, the nonexistence result for radially nonincreasing positive solutions of the system is implied. By using this nonexistence result, blow-up estimates for a class of quasilinear reaction–di$usion 11 systems (non-Newtonian 3ltration systems) are establish...

The present paper deals with a survey of various solutions of semi-linear, quasilinear and fully non-linear elliptic problems, developed by numerous researchers in a chronological order as the field developed year after year from 2000. Firstly we have collected some semi-linear, quasilinear and fully nonlinear elliptic models arising in different branches of science and engineering. Then a larg...

CONTENTS Introduction. 0. Pseudodifferential operators and linear PDE. §0.1 The Fourier integral representation and symbol classes §0.2 Schwartz kernels of pseudodifferential operators §0.3 Adjoints and products §0.4 Elliptic operators and parametrices §0.5 L 2 estimates §0.6 Gårding's inequality §0.7 The sharp Gårding inequality §0.8 Hyperbolic evolution equations §0.9 Egorov's theorem §0.10 M...

In this paper we obtain the interior C regularity of the quasilinear elliptic equations of divergence form. Our basic tools are the elementary local L estimates and weak Harnack inequality for second-order linear elliptic equations, and the compactness method.

This paper is devoted to the study, with variational technique, of the following quasilinear elliptic problem:

By using the weighted averaging techniques, we establish oscillation criteria for the second order damped quasilinear elliptic differential equation