Advances in Differential Equations

Singular solutions to a quasilinear {ODE}

Francesca Dalbono and M. García-Huidobro

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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.

Article information

Source
Adv. Differential Equations Volume 10, Number 7 (2005), 747-765.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867830

Mathematical Reviews number (MathSciNet)
MR2152351

Zentralblatt MATH identifier
1108.34023

Subjects
Primary: 34B16: Singular nonlinear boundary value problems
Secondary: 34B15: Nonlinear boundary value problems 35J60: Nonlinear elliptic equations

Citation

Dalbono, Francesca; García-Huidobro, M. Singular solutions to a quasilinear {ODE}. Adv. Differential Equations 10 (2005), no. 7, 747--765. https://projecteuclid.org/euclid.ade/1355867830.


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