## Differential and Integral Equations

### Multiple sign changing solutions in a class of quasilinear equations

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060870

Mathematical Reviews number (MathSciNet)
MR1870467

Zentralblatt MATH identifier
1020.34019

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

#### Citation

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