Multiple solutions of some semilinear elliptic equations via the generalized Conley index
The authors use the generalized Conley index to study the existence of several solutions of the problem \(-\Delta u= f(u)\), \(u|_{\partial D} =0\), where \(D\) is a bounded domain in \(\mathbb{R}^n\), and \(f\) is Lipschitz continuous with \(f(0) =0\). Two types of nonlinearities are considered. The first one has a jumping nonlinearity at zero and is sublinear at infinity. The second type is a conjugate case to the first one. In both cases three nontrivial solutions are obtained, one positive, one negative and one changing sign. Previously the existence of a changing sign solution was not known.
scientific article; zbMATH DE number 765102