A priori bounds and multiplicity of positive solutions for p-Laplacian Neumann problems with sub-critical growth

被引：12

作者：

Boscaggin, Alberto ^{[1
]}

Colasuonno, Francesca ^{[2
]}

Noris, Benedetta ^{[3
]}

机构：

[1] Univ Torino, Dipartimento Matemat, Via Carlo Alberto 10, I-10123 Turin, Italy

[2] Univ Bologna, Alma Mater Studiorum, Dipartimento Matemat, Piazza Porta S Donato 5, I-40126 Bologna, Italy

[3] Univ Picardie Jules Verne, Lab Amienois Math Fondamentale & Appliquee, 33 Rue St Leu, F-80039 Amiens, France

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2020年 / 150卷 / 01期

基金：

欧洲研究理事会;

关键词：

quasilinear elliptic equations; shooting method; a priori estimates; existence and multiplicity; Neumann boundary conditions; RADIALLY SYMMETRICAL-SOLUTIONS; CRITICAL EXPONENTS; DIRICHLET PROBLEM; EXISTENCE; EQUATIONS;

D O I：

10.1017/prm.2018.143

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let 1 < p < +8 and let O. RN be either a ball or an annulus. We continue the analysis started in [Boscaggin, Colasuonno, Noris, ESAIM Control Optim. Calc. Var. (2017)], concerning quasilinear Neumann problems of the type -Delta pu = f(u), u> 0 in O,..u = 0 on. O. We suppose that f(0) = f(1) = 0 and that f is negative between the two zeros and positive after. In case O is a ball, we also require that f grows less than the Sobolev-critical power at infinity. We prove a priori bounds of radial solutions, focussing in particular on solutions which start above 1. As an application, we use the shooting technique to get existence, multiplicity and oscillatory behaviour (around 1) of non-constant radial solutions.

引用

页码：73 / 102

页数：30

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