Analysis of an elliptic system with infinitely many solutions

被引：3

作者：

Cortazar, Carmen ^{[1
]}

Elgueta, Manuel ^{[1
]}

Garcia-Melian, Jorge ^{[2
,3
]}

机构：

[1] Pontificia Univ Catolica Chile, Fac Matemat, Dept Matemat, Casilla 306,Correo 22, Santiago, Chile

[2] Univ La Laguna, Dept Anal Matemat, C Astrofis Francisco Sanchez S-N, San Cristobal la Laguna 38200, Spain

[3] Univ La Laguna, Inst Univ Estudios Avanzados, Inst Univ Estudios Avanzados IUdEA Fis Atom Mol &, C Astrofis Francisco Sanchez S-N, San Cristobal la Laguna 38200, Spain

来源：

ADVANCES IN NONLINEAR ANALYSIS | 2017年 / 6卷 / 01期

关键词：

Elliptic system; infinitely many solutions; Harnack inequality; BOUNDARY-CONDITION; RESONANT SOLUTIONS; TURNING-POINTS; BIFURCATION; PARAMETER; EQUILIBRIA; EQUATIONS;

D O I：

10.1515/anona-2015-0151

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the elliptic system Delta u = u(p)v(q), Delta v = u(r)v(s) in Omega with the boundary conditions partial derivative u/partial derivative eta = lambda u, partial derivative v/partial derivative eta = mu v on partial derivative Omega, where Omega is a smooth bounded domain of R-N, p, s > 1, q, r > 0, lambda, mu > 0 and eta stands for the outward unit normal. Assuming the "criticality" hypothesis (p - 1)(s - 1)= qr, we completely analyze the values of lambda, mu for which there exist positive solutions and give a detailed description of the set of solutions.

引用

页码：1 / 12

页数：12

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