Multiple Sign Changing Radially Symmetric Solutions in a General Class of Quasilinear Elliptic Equations

In this paper we prove that the equation $ -( r^\alpha\phi(|u’®|)u’®)’ = \lambda r^\gamma f(u®), ~0<r<R$,where$\alpha, \gamma, {\bf{R}}$ are given real numbers, $\varphi :(0,\mathrm{\infty })\to (0,\mathrm{\infty })$ is a suitable twice differentiable function, $\lambda >0$ is a real parameter and $f:\mathbf{R}\to \mathbf{R}$ is continuous, admits an infinite sequence of sign-changing solutions satisfying $u^{\mathrm{\prime }}(0)=u(R)=0$. The function $f$ is required to satisfy $tf(t)>0$ for $t\mathrm{\ne }0$. Our technique explores fixed point arguments applied to suitable integral equations and shooting arguments. Our main result extends earlier ones in the case $\varphi$ is in the form $\phi(t) = |t|^{\beta}$foranappropriateconstant$\gamma$.