J. Aust. Math. Soc.  76 (2004), 125-140
Positive solutions of some quasilinear singular second order equations

J. V. Goncalves
  Universidade de Brasilia
  Departamento de Matemática
  70910-900 Brasilia (DF)
  Brazil
  jv@mat.unb.br
and
C. A. P. Santos
  Universidade Federal de Goiás
  Departamento de Matemática
  Catalao (GO)
  Brazil
  csantos@unb.br


Abstract
In this paper we study the existence and uniqueness of positive solutions of boundary value problems for continuous semilinear perturbations, say $f: [0,1)\times(0,\infty) \to (0,\infty)$, of a class of quasilinear operators which represent, for instance, the radial form of the Dirichlet problem on the unit ball of ${\mathbb{R}^N}$ for the operators: $p$-Laplacian ($1<p<\infty$) and $k$-Hessian ($1\leq k\leq N$). 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.
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