Nontrivial Solutions for a Class of Quasilinear Schrödinger Systems

Abstract

In this thesis, we research quasilinear Schrödinger system as follows in which 3<N∈R, 2<p<N, 2<q<N, V1(x),V2(x) are continuous functions, k,ι are parameters with k,ι>0, and nonlinear terms f,h∈C(RN×R2,R). We find a nontrivial solution (u,v) for all ι>ι1(k) by means of the mountain-pass theorem and change of variable theorem. Our main novelty of the thesis is that we extend Δ to Δp and Δq to find the existence of a nontrivial solution.