Global bifurcation for the H\'enon problem

Anna Lisa Amadori

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arXiv · 1909.01321

Global bifurcation for the H\'enon problem

Anna Lisa Amadori

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Abstract

We prove the existence of nonradial solutions for the H\'enon equation in the ball with any given number of nodal zones, for arbitrary values of the exponent $\alpha$. For sign-changing solutions, the case $\alpha=0$ -- Lane-Emden equation -- is included. The obtained solutions form global continua which branch off from the curve of radial solutions $p\mapsto u_p$, and the number of branching points increases with both the number of nodal zones and the exponent $\alpha$. The proof technique relies on the index of fixed points in cones and provides information on the symmetry properties of the bifurcating solutions and the possible intersection and/or overlapping between different branches, thus allowing to separate them at least in some cases.

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Anna Lisa Amadori. 2019-09-03. Global bifurcation for the H\'enon problem. https://arxiv.org/abs/1909.01321

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