A p-LAPLACIAN SUPERCRITICAL NEUMANN PROBLEM

被引：21

作者：

Colasuonno, Francesca ^{[1
]}

Noris, Benedetta ^{[1
]}

机构：

[1] Univ Libre Bruxelles, Dept Math, Campus Plaine CP214,Blvd Triomphe, B-1050 Brussels, Belgium

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2017年 / 37卷 / 06期

关键词：

Quasilinear elliptic equations; Sobolev-supercritical nonlinearities; Neumann boundary conditions; variational methods; RADIAL POSITIVE SOLUTIONS; ELLIPTIC-EQUATIONS; BOUNDARY-CONDITIONS; MULTIPLICITY; EXISTENCE; SYMMETRY; GROWTH;

D O I：

10.3934/dcds.2017130

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For p > 2, we consider the quasilinear equation Delta(p)u+\u\(p-2) u= g(u) in the unit ball B of R-N, with homogeneous Neumann boundary conditions. The assumptions on g are very mild and allow the nonlinearity to be possibly supercritical in the sense of Sobolev embeddings. We prove the existence of a nonconstant, positive, radially nondecreasing solution via variational methods. In the case g(u) = \u\ (q-2)u, we detect the asymptotic behavior of these solutions as q -> infinity.

引用

页码：3025 / 3057

页数：33