On the Existence of Radially Symmetric Solutions for the $ p $ -Laplace Equation with Strong Gradient Nonlinearities

Abstract

We consider the Dirichlet problem for the \( p \)-Laplace equation in presence of a gradient not satisfying the Bernstein–Nagumo type condition. We define some class of gradient nonlinearities, for which we prove the existence of a radially symmetric solution with a Hölder continuous derivative.