Multiplicity of solutions for some semi-linear elliptic systems with non-homogeneous boundary conditions

Abstract

In this article, we show that the existence of infinitely many weak solutions for some typical semi-linear elliptic systems governed by two Laplacian operators with non-homogeneous boundary conditions. A suitable perturbative method and variational tools will apply to such a non-symmetric problem: where Ω ⊂ RN , (N ≥ 3) is a smooth bounded domain. The results of existence are obtained when and α, β satisfy some conditions.