Multiple solutions for nonhomogeneous Schrodinger-Maxwell and Klein- Gordon-Maxwell equations on R 3

被引：35
|
作者：
Chen, Shang-Jie [1 ]
Tang, Chun-Lei [1 ]
机构：
[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China
来源：
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2010年 / 17卷 / 05期
基金：
中国国家自然科学基金;
关键词：
Schrodinger-Maxwell equations; Klein-Gordon-Maxwell equations; Nonhomogeneous; Superlinear; Ekeland's variational principle; Mountain Pass Theorem; Variational methods; SOLITARY WAVES; POSITIVE SOLUTIONS; POISSON EQUATIONS; GROUND-STATE; EXISTENCE; SYSTEM; NONEXISTENCE; FIELD; R-3;
D O I：
10.1007/s00030-010-0068-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we study the following nonhomogeneous Schrodinger-Maxwell equations {-Delta u + V(x)u + phi u = f(x, u) + h(x), in R-3, -Delta phi = u(2), in R-3, where f satisfies the Ambrosetti-Rabinowitz type condition. Under appropriate assumptions on V, f and h, the existence of multiple solutions is proved by using the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory. Similar results for the nonhomogeneous Klein-Gordon-Maxwell equations {-Delta u + [m(2) - (omega + phi)(2)]u = vertical bar mu vertical bar(q-2)u + h(x), in R-3, {-Delta phi + phi mu(2) = -omega mu(2), in R-3, are also obtained when 2 < q < 6.
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页码：559 / 574
页数：16
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