Multiple solutions for critical nonhomogeneous elliptic systems in noncontractible domain

Abstract

The paper is concerned with multiple solutions of a nonhomogeneous elliptic system with Sobolev critical exponent over a noncontractible domain, precisely, a smooth bounded annular domain. We prove the existence of four solutions using variational methods and Lusternik–Schnirelmann theory, when the inner hole of the annulus is sufficiently small.