Infinitely many nonradial solutions of a euclidean scalar field equation
We study the equation −Δu + b(|x|) u = ƒ(|x|, u), x ∈ RN;u ∈ H1(RN). The existence of a nonradial solution has been an open problem for some time even in the autonomous case. Under suitable hypotheses mainly on ƒ we find an unbounded sequence of nonradial solutions if N = 4 or N ≥ 6. We also obtain...
Gespeichert in:
| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
1993
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| In: |
Journal of functional analysis
Year: 1993, Jahrgang: 117, Heft: 2, Pages: 447-460 |
| ISSN: | 1096-0783 |
| DOI: | 10.1006/jfan.1993.1133 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1006/jfan.1993.1133 Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S002212368371133X 
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| Verfasserangaben: | T. Bartsch, M. Willem |
MARC
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| 520 | |a We study the equation −Δu + b(|x|) u = ƒ(|x|, u), x ∈ RN;u ∈ H1(RN). The existence of a nonradial solution has been an open problem for some time even in the autonomous case. Under suitable hypotheses mainly on ƒ we find an unbounded sequence of nonradial solutions if N = 4 or N ≥ 6. We also obtain infinitely many solutions if b and ƒ are not rotationally symmetric with respect to x but satisfy only a weaker symmetry. | ||
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