Multiplicity of critical points in presence of a linking: application to a superlinear boundary value problem
The author considers the following problem \[ -\Delta u-\lambda u=g(x,u),\text{ in }\Omega\quad u=0,\text{ on }\Omega,\tag{1} \] where \(\Omega\) is a smooth bounded domain of \(\mathbb R^N\), \(N\geq 3\), \(\lambda\in\mathbb R\) and \(g: \Omega\times \mathbb R\to\mathbb R\). The author is interested in a superlinear and subcritical cases. The author shows that for some values of \(\lambda\), problem (1) has at least three nontrivial solutions. To this end the author uses critical point theory.
scientific article; zbMATH DE number 2113836
scientific article