Solutions nodales sur les variétés Riemanniennes non localement conformément plates à bord

Abstract

Abstract. Dans cet article, on considère le problème de Dirichlet pour une EDP non linéaire avec une donnée au bord qui change de signe. L'existence d'une famille de solutions minimisantes est obtenue sur les variétés riemaniennes compactes non localement conformément platesà bord. This paper deals with solutions of Dirichlet problem for a nonlinear PDE with boundary data changing of sign. A family of minimizing nodal solutions are found on nonlocally conformally flat manifolds with boundary. Mathematics Subject Classification (2000). 53C21, 58J05.

Nodal solutions for fourth order elliptic equations with critical exponent on compact manifolds

“…In this paper we extend some results obtained by D. Holcman [19] for equations of the Yamabe type to the equations containing the operator of the Paneitz-Branson type. The main results of our study are summarized in the following theorem which is the version with boundary of Theorem 3 of Episoto-Robert [15].…”