Radial Positive Solutions for p-Laplacian Supercritical Neumann Problems

• Main Authors: Francesca Colasuonno, Benedetta Noris
• Format: Article
• Language: English
• Published: University of Bologna 2017-12-01
• Series: Bruno Pini Mathematical Analysis Seminar
• Subjects: Quasilinear elliptic equations; Shooting method; Variational methods; Sobolev-supercritical nonlinearities; Neumann boundary conditions
• Online Access: https://mathematicalanalysis.unibo.it/article/view/7797

This paper deals with existence and multiplicity of positive solutions for a quasilinear problem with Neumann boundary conditions. The problem is set in a ball and admits at least one constant non-zero solution; moreover, it involves a nonlinearity that can be supercritical in the sense of Sobolev embeddings. The main tools used are variational techniques and the shooting method for ODE's. These results are contained in A. Boscaggin, F. Colasuonno, B. Noris. Multiple positive solutions for a class of p-Laplacian Neumann problems without growth conditions. ESAIM Control Optim. Calc. Var., DOI: 10.1051/cocv/2016064 (2017; F. Colasuonno, B. Noris. A p-Laplacian supercritical Neumann problem. Discrete Contin. Dyn. Syst., 37 (2017) 3025-3057.