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2002 Multiple sign changing solutions in a class of quasilinear equations
J. V. Goncalves, A. L. Melo
Differential Integral Equations 15(2): 147-165 (2002).

Abstract

This paper deals with finding multiple sign-changing solutions of the following class of quasilinear problems: $$ \begin{cases} - (r^{\alpha} |u'(r)|^{\beta}u'(r))^{'} = \lambda~ r^{\gamma} f(u(r)),~~ 0 < r < R\\ u(R)= u'(0)=0 , \end{cases} $$ where $\alpha,$ $\beta$ and $\gamma$ are given real numbers, $\lambda > 0$ is a parameter, $f: {\bf R} \to {\bf R}$ is some continuous function and $0 < R < \infty$. A result on existence of infinitely many sign-changing solutions is obtained by considering a family of associated initial value problems which are solved through a shooting argument and a counting of zeroes.

Citation

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J. V. Goncalves. A. L. Melo. "Multiple sign changing solutions in a class of quasilinear equations." Differential Integral Equations 15 (2) 147 - 165, 2002.

Information

Published: 2002
First available in Project Euclid: 21 December 2012

zbMATH: 1020.34019
MathSciNet: MR1870467

Subjects:
Primary: 35J60
Secondary: 34B15

Rights: Copyright © 2002 Khayyam Publishing, Inc.

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Vol.15 • No. 2 • 2002
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