Analysis of an elliptic system with infinitely many solutions

作者：Cortazar Carmen; Elgueta Manuel; Garcia Melian Jorge^*

来源：Advances in Nonlinear Analysis, 2017, 6(1): 1-12.

DOI：10.1515/anona-2015-0151

• Elliptic system
• infinitely many solutions
• Harnack inequality

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.

• 出版日期2017-2