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Nonautonomous and non periodic Schrödinger equation with indefinite linear part

  • L. A. Maia
  • J. C. Oliveira Junior
  • R. Ruviaro
Article

Abstract

The existence of solution of the nonlinear Schrödinger equation
$$\begin{aligned} \begin{array}{lc} -\Delta u + V(x) u = f(x,u),&\end{array} \end{aligned}$$
is stablished in \(\mathbb {R}^N\), where V changes sign and f is an asymptotically linear function at infinity, with V and f non periodic in x. Spectral theory, a classical linking theorem and interaction between translated solutions of the problem at infinity are employed.

Keywords

Asymptotically linear Linking theorem Spectral theory 

Mathematics Subject Classification

35J20 35J60 35Q55 

Notes

Acknowledgments

The authors thank Professor Charles A. Stuart for elucidating many doubts in the spectral theory employed in the development of this work.

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • L. A. Maia
    • 1
  • J. C. Oliveira Junior
    • 2
  • R. Ruviaro
    • 1
  1. 1.Departamento de MatemáticaUniversidade de BrasíliaBrasíliaBrazil
  2. 2.Universidade Federal do TocantinsPalmasBrazil

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