Multiple nontrivial solutions of elliptic semilinear equations (Q5929984)

Let \(\Omega\) be a smooth, bounded domain in \(\mathbb{R}^N\) and let \(A\) be a selfadjoint operator on \(L^2(\Omega)\). The paper deals with the study of the semilinear problem \(Au=f(x,u)\), \(u\in D(|A|^{1/2})\). The main result of this work establishes the existence of multiple nontrivial solutions to the above problem, provided the corresponding energy functional exhibits local splitting at zero. The approach is variational and is based on the critical point theorems of Brezis-Nirenberg and Perera.