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Positive solutions of some quasilinear singular second order equations

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  09 April 2009

J. V. Goncalves  and
C. A. P. Santos
J. V. Goncalves
Affiliation:
Universidade de Brasilia, Departamento de Matemática, 70910-900 Brasilia(DF), Brazil, e-mail: jv@mat.unb.br
C. A. P. Santos
Affiliation:
Universidade Federal de Goiás, Departmento de Matemática Catalão(GO), Brazil, e-mail: csantos@unb.br
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Abstract

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In this paper we study the existence and uniqueness of positive solutions of boundary vlue problems for continuous semilinear perturbations, say f: [0, 1) × (0, ∞) → (0, ∞), of class of quasilinear operators which represent, for instance, the radial form of the Dirichlet problem on the unit ball of RN for the operators: p-Laplacian (1 < p < ∞) ad 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.

Keywords

quasilinear singular eqationsraidal positive solutionsfixed pointsshooting mehtod

MSC classification

Secondary: 35J25: Boundary value problems for second-order elliptic equations 35J65: Nonlinear boundary value problems for linear elliptic equations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 76 , Issue 1 , February 2004 , pp. 125 - 140
Copyright
Copyright © Australian Mathematical Society 2004

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