Differential and Integral Equations

Multiple sign changing solutions in a class of quasilinear equations

J. V. Goncalves and A. L. Melo

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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.

Article information

Differential Integral Equations, Volume 15, Number 2 (2002), 147-165.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations
Secondary: 34B15: Nonlinear boundary value problems


Goncalves, J. V.; Melo, A. L. Multiple sign changing solutions in a class of quasilinear equations. Differential Integral Equations 15 (2002), no. 2, 147--165. https://projecteuclid.org/euclid.die/1356060870

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