Some Elliptic Problems With Nonlinear Boundary Conditions


Dpto. Ecuaciones Diferenciales y Análisis Numérico, C/ Tarfia s/n, 41080, Univ. of Sevilla, Seville, Spain E-mails: [email protected] and [email protected]

In memory of Prof. J. Esquinas

This paper concerns with some elliptic equations with non-linear boundary conditions. Sub-supersolution and bifurcation methods are used in order to obtain existence, uniqueness or multiplicity of positive solutions.

1. Introduction

In this paper we study positive solutions of some nonlinear elliptic problems with mixed nonlinear boundary conditions. Throughout it, we consider the following assumptions:

(1) ÍÍC M.N, N > 1, is a bounded domain with boundary dil of class C2. Moreover, where To and Ti denote two disjoint open and closed sets in the relative topology of dil.

(2) L is a uniformly elliptic differential operator in Q of the form with coefficients ay = aj¿ € C2>a(ft), bi G C1>a(fi) and c € Ca(fi), a G (0,1).

•Supported by the Spanish Ministry of Science and Technology under grant BFM2003-06446.

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