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.

Bifurcation analysis of the Hardy-Sobolev equation / Bonheure, D.; Casteras, J. -B.; Gladiali, F.. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 296:(2021), pp. 759-798. [10.1016/j.jde.2021.06.012]

Bifurcation analysis of the Hardy-Sobolev equation

Gladiali F.
2021

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11388/253778
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