EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO NONLINEAR RADIAL p-LAPLACIAN EQUATIONS

This article concerns the existence, uniqueness and boundary behavior of positive solutions to the nonlinear problem 1/A (A Phi(p)(u'))' + a(1)(x)u(alpha 1) + a(2)(x)u(alpha 2) = 0, in (0, 1), lim(x -> 0) A Phi(p)(u')(x) = 0, u(1) = 0, where p > 1, alpha(1), alpha(2) is an element of (1 - p, p - 1), Phi(p)(t) = t vertical bar t vertical bar(p-2), t is an element of R, A is a positive differentiable function and a(1), a(2) are two positive measurable functions in (0, 1) satisfying some assumptions related to Karamata regular variation theory.