Quasilinear Elliptic Equations In Existence And Non-existence Of The Study

In this paper, we investigate some results of solutions to two kinds of quasilinear elliptic equations. This investigation contains the existence, nonexistence and multi-plicity of positive solutions, etc.In chapter1, we consider the following quasilinear elliptic problem where λ∈R, Δp=div(|(?)u|p-2(?)u),1<p<N,0<q<p-1<r≤p*-1. We give some sufficient conditions for existence, nonexistence and multiplicity of nonnegative solutions, by means of upper and lower solution method and the mountain pass theorem.In chapter2, we consider the quasilinear nonpositone elliptic equation where p>1, λ>0, Ω denotes a ball in RN(N≥2);f has more than one zero and f(0)<0(the nonpositone case). We investigate the existence of radial positive solutions for the quasilinear elliptic equations nonpositone problems in a ball.In chapter3, we consider the quasilinear nonpositone elliptic equation where p>1,λ>0, Ω denotes an annulus in RN(N>2),f(0)<0(the nonpositone case) and f has more than one zero. We give a sufficient condition for the nonexistence of radial positive solutions.