Multiplicity of nontrivial solutions of semilinear elliptic equations
It is considered the following problem: \(-\Delta u = f(x,u)\) in \(\Omega\), \(u=0\) on \(\partial\Omega\), where \(f\) is a subcritical Carathéodory function. It is proved the existence of at least two nontrivial solutions. This paper unifies and generalizes some results from \textit{A. Castro} and \textit{A. C. Lazer} [Ann. Mat. Pura Appl., IV. Ser. 120, 113-137 (1979; Zbl 0426.35038)] as well as from \textit{N. Hirano} and \textit{T. Nishimura} [J. Math. Anal. Appl. 180, No. 2, 566-586 (1993; Zbl 0835.35052)].
scientific article; zbMATH DE number 1533168