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 ⊂ R^N , (N ≥ 3) is a smooth bounded domain. The results of existence are obtained when and α, β satisfy some conditions.

Keywords:

• Elliptic equation systems
• Critical point theory
• Perturbation methods

Acknowledgments

Thanks for the guidance and encouragement of Professor Ai Nong Fang. Project supported by NSFC (10271077).