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March/April 2018 Nodal solutions for Lane-Emden problems in almost-annular domains
Anna Lisa Amadori, Francesca Gladiali, Massimo Grossi
Differential Integral Equations 31(3/4): 257-272 (March/April 2018).

Abstract

In this paper, we prove an existence result to the problem $$\left\{\begin{array}{ll} -\Delta u = |u|^{p-1} u \qquad & \text{ in } \Omega , \\ u= 0 & \text{ on } \partial\Omega, \end{array} \right. $$ where $\Omega$ is a bounded domain in $\mathbb R^{N}$ which is a perturbation of the annulus. Then there exists a sequence $p_1 < p_2 < \cdots$ with $\lim\limits_{k\rightarrow+\infty}p_k=+\infty$ such that for any real number $p > 1$ and $p\ne p_k$ there exist at least one solution with $m$ nodal zones. In doing so, we also investigate the radial nodal solution in an annulus: we provide an estimate of its Morse index and analyze the asymptotic behavior as $p\to 1$.

Citation

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Anna Lisa Amadori. Francesca Gladiali. Massimo Grossi. "Nodal solutions for Lane-Emden problems in almost-annular domains." Differential Integral Equations 31 (3/4) 257 - 272, March/April 2018.

Information

Published: March/April 2018
First available in Project Euclid: 19 December 2017

zbMATH: 06837097
MathSciNet: MR3738198

Subjects:
Primary: 35B05, 35J91

Rights: Copyright © 2018 Khayyam Publishing, Inc.

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Vol.31 • No. 3/4 • March/April 2018
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