Nontrivial solution of a semilinear schrödinger equation
- 1 January 1996
- journal article
- research article
- Published by Taylor & Francis in Communications in Partial Differential Equations
- Vol. 21 (9-10) , 1431-1449
- https://doi.org/10.1080/03605309608821233
Abstract
This paper deals with strongly indefinite functionals whose gradients are Fredholm operators of index 0 and map weakly convergent sequences to weakly convergent sequences. We show how these results apply to a ZN—invariant semilinear Schrödinger equation on RN.Keywords
This publication has 13 references indexed in Scilit:
- Homoclinic orbits on compact hypersufaces in 293-1293-1293-1, of restricted contact typeCommunications in Mathematical Physics, 1995
- Stationary states of the nonlinear Dirac equation: A variational approachCommunications in Mathematical Physics, 1995
- Solutions in Spectral Gaps for a Nonlinear Equation of Schrödinger TypeJournal of Differential Equations, 1994
- Spatial gap solitons in periodic nonlinear structuresOptics Letters, 1993
- Existence of a nontrivial solution to a strongly indefinite semilinear equationProceedings of the American Mathematical Society, 1993
- Existence and bifurcation of solutions for nonlinear perturbations of the periodic Schrödinger equationJournal of Differential Equations, 1992
- Existence of solutions for semilinear elliptic equations with indefinite linear partJournal of Differential Equations, 1992
- Periodic solutions on hypersurfaces and a result by C. ViterboInventiones Mathematicae, 1987
- Critical point theorems for indefinite functionalsInventiones Mathematicae, 1979
- Approximation de fonctions différentiables sur certains espaces de BanachAnnales de l'institut Fourier, 1971