A sub-supersolution approach for Neumann boundary value problems with gradient dependence. (English) Zbl 1437.35357
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.
Reviewer: Vicenţiu D. Rădulescu (Craiova)
MSC:
| 35J62 | Quasilinear elliptic equations |
| 58E05 | Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces |
Keywords:
quasilinear elliptic equation; Neumann problem; gradient dependence; sub-supersolution; positive solutionReferences:
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