Our concern is on existence, uniqueness and regularity of convex, negative, radially symmetric classical solutions towhere |x| is the euclidean norm of x. The main interest is in the case ψ is singular at |x| = 1 and/or u = 0, although several nonsingular cases are covered by the main result. Our approach to show existence, exploits fixed point arguments and the shooting method. Uniqueness and regularity are achieved through suitable estimates. 2004 Elsevier Inc. All rights reserved.
In this paper we study the existence and uniqueness of positive solutions of boundary value problems for continuous semilinear perturbations, say / : [0, 1) x (0, oo) -* (0, oo), of a class of quasilinear operators which represent, for instance, the radial form of the Dirichlet problem on the unit ball of R* for the operators: p-Laplacian (1 < p < oo) and k-Hessian (1 < k < N). As a key feature, f(r, u) is possibly singular at r = 1 or u = 0. Our approach exploits fixed point arguments and the Shooting Method.2000 Mathematics subject classification: primary 35J25, 35J65.
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