The critical Neumann problem for semilinear elliptic equations with concave perturbations
This paper deals with the qualitative analysis of a Neumann semilinear elliptic problem on a bounded domain with smooth boundary. The main feature of this work consists in the presence of a critical nonlinearity (in the Sobolev sense) combined with an indefinite weight function and a concave perturbation. A first result establishes the existence of a solution which is obtained through a local minimization. Next, by means of the concentration-compactness principle and a careful analysis of energy levels of the associated energy functional, the author establishes the existence of a second distinct solution. An interesting relationship between the shape of the variable potential and the mean curvature of the boundary is also established in the present paper.
scientific article; zbMATH DE number 5292357
scientific article