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.