Infinitely many solutions for some nonlinear elliptic problems in symmetrical domains

Abstract

Synopsis We consider the boundary value problem where Ω ⊂ ℝ n is a bounded domain, n ≧3, 2* = 2 n /( n − 2) is the critical exponent for the Sobolev embedding and λ is a real positive parameter. We prove the existence of infinitely many solutions of (*) when Ω exhibits suitable symmetries.