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)
C. A. P. Santos
  Universidade Federal de Goiás
  Departamento de Matemática
  Catalao (GO)

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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