A sub-supersolution approach for Neumann boundary value problems with gradient dependence (Q1987394)

This paper is concerned with the qualitative analysis of solutions for a class of quasilinear elliptic problems with Neumann boundary condition. A feature of this paper is the presence of a very general differential operator and the competition effects created by a reaction with gradient term and a power-type nonlinearity. The authors are concerned with the existence and location of solutions by using a non-variational approach based on an adequate method of sub-supersolution. The main abstract results of this paper is applied to establish the existence of finitely many positive solutions or even infinitely many positive solutions for a class of Neumann problems.