On the Existence of Radially Symmetric Solutions for the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$ p $\\end{document}-Laplace Equation with Strong Gradient Nonlinearities

Abstract

We consider the Dirichlet problem for the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$ p $\\end{document}-Laplace equationin 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.