MULTIPLE POSITIVE SOLUTIONS FOR SCHRODINGER-POISSON SYSTEM IN R3 INVOLVING CONCAVE-CONVEX NONLINEARITIES WITH CRITICAL EXPONENT

作者：Li, Miao-Miao; Tang, Chun-Lei^*

来源：Communications on Pure and Applied Analysis, 2017, 16(5): 1587-1602.

DOI：10.3934/cpaa.2017076

• Schrodinger-Poisson system
• Mountain Pass Theorem
• Ekeland's variational principle
• critical exponent
• concentration compactness principle

In this paper, we study the existence of multiple positive solutions of the following Schrodinger-Poisson system with critical exponent @@@ { -Delta u - l(x)phi u = lambda h(x)vertical bar u vertical bar(q-2)u + vertical bar u vertical bar(4)u, in R-3, @@@ -Delta phi = l(x)u(2), in R-3, @@@ where 1 < q < 2 and lambda > 0. Under some appropriate conditions on l and h, we show that there exists lambda* > 0 such that the above problem has at least two positive solutions for each lambda is an element of (0, lambda*) by using the Mountain Pass Theorem and Ekeland's Variational Principle.

• 出版日期2017-9
• 单位西南大学