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On perturbation of a functional with the mountain pass geometry

Applications to the nonlinear Schrödinger–Poisson equations and the nonlinear Klein–Gordon–Maxwell equations
  • Wonjeong Jeong
  • Jinmyoung SeokEmail author
Article

Abstract

Consider a functional \(I_0\) with the mountain-pass geometry and a critical point \(u_0\) of mountain-pass type. In this paper, we discuss about the existence of critical points \(u_\varepsilon \) around \(u_0\) for functionals \(I_\varepsilon \) perturbed from \(I_0\) in a suitable sense. As applications, we show the existence of a solution to the nonlinear Schrödinger–Poisson equations and the nonlinear Klein–Gordon–Maxwell equations with quite general class of nonlinearity.

Mathematics Subject Classification (2000)

35A15 35B38 35J50 

Notes

Acknowledgments

The authors would like to express sincere gratitude to their advisor Prof. Byeon for his direction and encouragement. The first author was supported by Basic Science Research Program (No. 2011-0030749) and Mid-career Researcher Program (No. 2010-0014135) through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (MEST). The second author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2012-0000941).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of MathematicsPOSTECHPohangRepublic of Korea
  2. 2.Department of Mathematical ScienceSeoul National UniversitySeoulRepublic of Korea

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