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
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页码：1 / 12
页数：12
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