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QUASILINEAR PROBLEMS WITH THE COMPETITION BETWEEN CONVEX AND CONCAVE NONLINEARITIES AND VARIABLE POTENTIALS

DRAGOS-PATRU COVEI

Constantin Brancusi University of Tg-Jiu, Str. Grivitei, No 1, Tg-Jiu, Gorj, Romania

https://doi.org/10.1142/S0129167X13500055Cited by:1 (Source: Crossref)

Abstract

The purpose of this paper is to prove some existence and non-existence theorems for the nonlinear elliptic problems of the form -Δ_pu = λk(x)u^q ± h(x)u^σ if x ∈ Ω, subject to the Dirichlet condition u = 0 on ∂Ω. In the proof of our results we use the sub-solution, super-solution methods and variational arguments.

Keywords:

AMSC: 35J60, 35J20, 35A05

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