A multiplicity result for the scalar field equation
| Autor: | Perera Kanishka |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Advances in Nonlinear Analysis, Vol 3, Iss S1, Pp s47-s54 (2014) |
| Druh dokumentu: | article |
| ISSN: | 2191-9496 2191-950X |
| DOI: | 10.1515/anona-2014-0022 |
| Popis: | We prove the existence of N - 1 distinct pairs of nontrivial solutions of the scalar field equation in ℝN under a slow decay condition on the potential near infinity, without any symmetry assumptions. Our result gives more solutions than the existing results in the literature when N ≥ 6. When the ground state is the only positive solution, we also obtain the stronger result that at least N - 1 of the first N minimax levels are critical, i.e., we locate our solutions on particular energy levels with variational characterizations. Finally we prove a symmetry breaking result when the potential is radial. To overcome the difficulties arising from the lack of compactness we use the concentration compactness principle of Lions, expressed as a suitable profile decomposition for critical sequences. |
| Databáze: | Directory of Open Access Journals |
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