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

作者：Chen, Shang-Jie; Tang, Chun-Lei^*

来源：Nodea-Nonlinear Differential Equations and Applications, 2010, 17(5): 559-574.

DOI：10.1007/s00030-010-0068-z

• Schrodinger-Maxwell equations
• Klein-Gordon-Maxwell equations
• Nonhomogeneous
• Superlinear
• Ekeland's variational principle
• Mountain Pass Theorem
• Variational methods

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.

• 出版日期2010-10
• 单位西南大学