Bifurcation analysis of the Hardy-Sobolev equation
| Autor: | Jean-Baptiste Casteras, Francesca Gladiali, Denis Bonheure |
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| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Applied Mathematics Operator (physics) Hardy-Sobolev inequality 010102 general mathematics Monotonic function 01 natural sciences Morse index 010101 applied mathematics Sobolev space Bifurcation analysis Mathematics - Analysis of PDEs Symmetry and monotonicity of solutions Kernel (statistics) FOS: Mathematics 0101 mathematics Analyse mathématique Positive solutions Analysis Mathematics Analysis of PDEs (math.AP) |
| Zdroj: | Journal of differential equations, 296 |
| DOI: | 10.48550/arxiv.2009.04195 |
| Popis: | In this paper, we prove existence of multiple non-radial solutions to the Hardy-Sobolev equation [Formula presented] where N≥3, s∈[0,2), [Formula presented] and [Formula presented]. We extend results of E.N. Dancer, F. Gladiali, M. Grossi (2017) [12] where only the case s=0 is considered. The results specially rely on a careful analysis of the kernel of the linearized operator. Moreover, thanks to monotonicity properties of the solutions, we separate two branches of non-radial solutions. SCOPUS: ar.j info:eu-repo/semantics/published |
| Databáze: | OpenAIRE |
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