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2005 Singular solutions to a quasilinear {ODE}
Francesca Dalbono, M. García-Huidobro
Adv. Differential Equations 10(7): 747-765 (2005).

Abstract

In this paper, we prove the existence of infinitely many radial solutions having a singular behaviour at the origin for a superlinear problem of the form $-\Delta_pu=|u|^{\delta-1}u$ in $B(0,1)\setminus\{0\}\subset\mathbb R^N$,\, $u=0$ for $|x|=1$, where $N>p>1$ and $\delta>p-1$. Solutions are characterized by their nodal properties. The case $\delta+1 <\frac{Np}{N-p}$ is treated. The study of the singularity is based on some energy considerations and takes into account the classification of the behaviour of the possible solutions available in the literature. By following a shooting approach, we are able to deduce the main multiplicity result from some estimates on the rotation numbers associated to the solutions.

Citation

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Francesca Dalbono. M. García-Huidobro. "Singular solutions to a quasilinear {ODE}." Adv. Differential Equations 10 (7) 747 - 765, 2005.

Information

Published: 2005
First available in Project Euclid: 18 December 2012

zbMATH: 1108.34023
MathSciNet: MR2152351

Subjects:
Primary: 34B16
Secondary: 34B15, 35J60

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.10 • No. 7 • 2005
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