Infinitely many radial solutions for a sub-super critical p-Laplacian problem

We prove the existence of infinitely many sign-changing radial solutions for a p-sub-super critical p-Laplacian Dirichlet problem in a ball. We consider an equation defined by the p-Laplacian operator perturbed by a nonlinearity g(u) that is p-subcritical at \(+\,\infty \) and p-supercritical at \(-\,\infty \). Our results extend those in Castro et al. (Electron. J. Differ. Equ. 2007(111):1–10, 2007) for the corresponding semilinear case and those of El Hachimi and De Thelin (J. Differ. Equ. 128:78–102, 1996) where the subcritical case was studied.