Existence and multiplicity of non-trivial solutions for a class of modified Schrodinger-Poisson systems

[摘要] In the present paper, we study the following modified Schrodinger-Poisson system {-Delta u + V(x)u + phi u - 1/2u Delta u(2) =vertical bar u vertical bar(p-1) u + h(x), in R-3, -Delta phi = mu(2), in R-3, where 4 <= p + 1 < 12, h is an element of L-2(R-3) and h not equal 0. This model describes the interaction of a charge particle with an electro-magnetic field. Under some hypotheses on V(x), we prove the existence of a non-trivial ground state solution and two non-trivial ground state solutions for the system (P). (C) 2013 Elsevier Inc. All rights reserved.

[发布日期] 2013-12-15

[关键词] Modified Schrodinger-Poisson system;Sobolev embedding;Minimizer