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2002 Multiplicity results in a ball for $p$-Laplace equation with positive nonlinearity
S. Prashanth, K. Sreenadh
Adv. Differential Equations 7(7): 877-896 (2002). DOI: 10.57262/ade/1356651709

Abstract

We consider the equation $-\Delta_{p}u=u^{\alpha}+u^{q}$ where $0\le q <p-1 <\alpha\le p^{*}-1$ in the ball $B_{R}(0)\subset \mathbb R^{N}, N\ge 2.$ Here, $p^{*}=Np/(N-p)$. We show the existence of at least two positive solutions to the above equation for small enough balls when $\alpha=p^{*}-1$ and $q>0.$ Further if $p\in (1,2)$ and $\alpha\le p^{*}-1$, we show the existence of exactly two positive solutions for small enough balls when $q>0$, and at most two solutions when $q=0$. This we do by the asymptotic analysis of the corresponding Emden-Fowler equation.

Citation

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S. Prashanth. K. Sreenadh. "Multiplicity results in a ball for $p$-Laplace equation with positive nonlinearity." Adv. Differential Equations 7 (7) 877 - 896, 2002. https://doi.org/10.57262/ade/1356651709

Information

Published: 2002
First available in Project Euclid: 27 December 2012

zbMATH: 1033.35039
MathSciNet: MR1895169
Digital Object Identifier: 10.57262/ade/1356651709

Subjects:
Primary: 35J65
Secondary: 34B15 , 35B33 , 35J60

Rights: Copyright © 2002 Khayyam Publishing, Inc.

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Vol.7 • No. 7 • 2002
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