Multiplicity results for nonlinear elliptic equations

Abstract

Let $Omega$ be a bounded domain in $mathbb{R}^{N}$, $Ngeq 3$, and $p=frac{2N}{N-2}$ the limiting Sobolev exponent. We show that for $fin H^1_0(Omega)^ast$, satisfying suitable conditions, the nonlinear elliptic problem $$displaylines{ -Delta u =|u |^{ p-2 }u +f quad hbox{in } Omega cr u=0 quad hbox{on } partialOmega }$$ has at least three solutions in $H_{0}^{1}(Omega)$.

Keywords

• Semilinear elliptic equations
• critical Sobolev exponent.