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...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
1993
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| In: |
Journal of functional analysis
Year: 1993, Volume: 117, Issue: 2, Pages: 447-460 |
| ISSN: | 1096-0783 |
| DOI: | 10.1006/jfan.1993.1133 |
| Online Access: | 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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| Author Notes: | T. Bartsch, M. Willem |
| Summary: | 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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| Item Description: | Elektronische Reproduktion der Druck-Ausgabe 25. Mai 2002 Gesehen am 12.06.2023 |
| Physical Description: | Online Resource |
| ISSN: | 1096-0783 |
| DOI: | 10.1006/jfan.1993.1133 |