On stationary points of nonexpansive set-valued mappings

In this paper we deal with stationary points (also known as endpoints) of nonexpansive set-valued mappings and show that the existence of such points under certain conditions follows as a consequence of the existence of approximate stationary sequences. In particular we provide abstract extensions of well-known fixed point theorems.Dirección General de Enseñanza SuperiorJunta de Andalucí

ON THE 1ST CURVE OF THE FUCIK SPECTRUM OF AN ELLIPTIC OPERATOR

We obtain a variational characterization of the first nontrivial curve in the Fucik spectrum of the Laplacian. We study the asymptotic behaviour of this curve and exhibit a connexion with the antimaximum principle. An application is given to a nonresonance problem.316121295129

A nodal domain property for the p-Laplacian

We show a partial version of the Courant nodal domain theorem for the p-Laplacian: any eigenfunction associated to the second eigenvalue has exactly two nodal domains. A similar result is also proved for the Fucik spectrum. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.330866967

The beginning of the Fucik spectrum for the p-Laplacian

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On the Fucik spectrum of the p-Laplacian

We prove the existence of a first non-trivial curve in the Fucik spectrum of the p-Laplacian. This yields in particular a variational characterization of the second eigenvalue of the p-Laplacian by a mountain pass procedure. An application to the study of the existence of solution for an equation of the form-Delta(p)u = f(x, u) is given. (C) Academie des Sciences/Elsevier, Paris.326668168