Hostname: page-component-848d4c4894-hfldf Total loading time: 0 Render date: 2024-05-09T04:18:54.460Z Has data issue: false hasContentIssue false
  • English
  • Français

MULTIPLICITY RESULTS FOR A PERTURBED NONLINEAR SCHRÖDINGER EQUATION

Published online by Cambridge University Press:  01 September 2007

F. CAMMAROTO ,
A. CHINNÌ  and
B. DI BELLA
F. CAMMAROTO*
Affiliation:
Department of Mathematics, University of Messina, 98166 Sant'Agata-Messina, Italy e-mail: filippo@dipmat.unime.it
A. CHINNÌ
Affiliation:
Department of Mathematics, University of Messina, 98166 Sant'Agata-Messina, Italy e-mail: filippo@dipmat.unime.it
B. DI BELLA
Affiliation:
Department of Mathematics, University of Messina, 98166 Sant'Agata-Messina, Italy e-mail: filippo@dipmat.unime.it
*
*Corresponding author. Because of a surprising coincidence of names within the same Department, we have to point out that the author was born on August 4, 1968.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, using a recent critical point theorem of Ricceri, we establish two multiplicity results for the Schrödinger equation of the form where are Carathéodory functions, λ and μ two positive parameters.

Keywords

35Q55.
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 49 , Issue 3 , September 2007 , pp. 423 - 429
Copyright
Copyright © Glasgow Mathematical Journal Trust 2007

References

REFERENCES

1.Bartsch, T., Pankov, A. and Wang, Z.-Q., Nonlinear Schrödinger equations with steep potential well. Comm. Contemp. Math. 4 (2001), 549–569.CrossRefGoogle Scholar
2.Bartsch, T., Liu, Z. and Weth, T., Sign changing solutions of superlinear Schrödinger equations, Comm. Partial Differential Equations, 29 (2004), 25–42.Google Scholar
3.Bonanno, G., Some remarks on a three critical points theorem, Nonlinear Analysis, 54 (2003), 651–665.CrossRefGoogle Scholar
4.Kristály, A., Multiple solutions for a sublinear Schrödinger equation, NoDEA: Nonlinear Differential Equations 14 (2007), 291–302.CrossRefGoogle Scholar
5.Pucci, P. and Serrin, J., A mountain pass theorem, J. Differential Equations 60 (1985), 142–149.CrossRefGoogle Scholar
6.Rabinowitz, P. H., On a class of nonlinear Schrödinger equations, Z. Angew. Math. Phys. 43 (1992), 270–291.CrossRefGoogle Scholar
7.Ricceri, B., Existence of three solutions for a class of elliptic eigenvalue problems, Math. Comput. Modelling 32 (2000), 1485–1494.CrossRefGoogle Scholar
8.Ricceri, B., Minimax theorems for limits of parametrized functions having at most one local minimum lying in a certain set, Topology Appl., 153 (2006), 3308–3312.CrossRefGoogle Scholar
9.Zeidler, E., Nonlinear functional analysis and applications, Vol. III. (Springer-Verlag, 1985).Google Scholar