Zeitschrift für angewandte Mathematik und Physik

, Volume 64, Issue 5, pp 1413–1442 | Cite as

Multibump solutions for discrete periodic nonlinear Schrödinger equations

  • Shiwang Ma
  • Zhi-Qiang Wang


In this paper, we study the existence of multibump solutions for discrete nonlinear Schrödinger equations with periodic potentials. We first reduce the existence of multibump homoclinic solutions to the existence of an isolated homoclinic solution with a nontrivial critical group. Then, we study the existence of homoclinics with nontrivial critical groups for both superlinear and asymptotically linear discrete periodic nonlinear Schrödinger equations, and we provide simple sufficient conditions for the existence of homoclinics with nontrivial critical groups in the positive definite case. As an application, we get, without any symmetry assumptions, infinitely many geometrically distinct homoclinic solutions with exponential decay at infinity.

Mathematics Subject Classification (2000)

35Q55 35Q51 39A12 39A70 78A40 


Discrete Schrödinger equation with periodic potential Homoclinic solution Multibump solution Critical group 


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Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.School of Mathematical Sciences and LPMCNankai UniversityTianjinPeople’s Republic of China
  2. 2.Chern Institute of Mathematics and LPMCNankai UniversityTianjinPeople’s Republic of China
  3. 3.Department of Mathematics and StatisticsUtah State UniversityLoganUSA

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