On the construction of Ljusternik-Schnirelmann critical values in Banach spaces (Q1187242)

The main goal of this paper is to extend to some Banach spaces iterative methods already known for Hilbert spaces in order to obtain all the critical values arising in the framework of Ljusternik-Schnirelman critical point theory. This is done for uniformly convex Banach spaces \(E\) such that the dual space \(E^*\) has the same property. If \(J: E\to E^*\) is the duality mapping, then the nonlinear eigenvalue problem \(g'(x)=\mu J(x)\) is considered for \(g\in C^ 1(E,\mathbb{R})\) satisfying rather general assumptions. An application to nonlinear partial differential equations involving the so-called \(p\)-Laplacian operator is given.