A Ljusternik–Schnirelmann type theorem for eigenvalues of a prescribed mean curvature problem Original Research Article

This paper is about the following eigenvalue problem: View the MathML source-div∇u1+|∇u|2=λg(x,u)inΩ,u=0on∂Ω. Turn MathJax on By using a Ljusternik–Schnirelmann theory for variational inequalities in a space of functions of bounded variation, we show the existence of infinite sequences of eigenvalues and eigenfunctions on each level of the area functional. Properties and finite dimensional approximation of these eigenvalues and eigenfunctions are also described.