Electron. J. Diff. Eqns., Vol. 2002(2002), No. 78, pp. 1-15.

Boundary behavior of blow-up solutions to some weighted non-linear differential equations

Ahmed Mohammed

Abstract:
We investigate, under appropriate conditions on the weight $g$ and the non-linearity $f$, the boundary behavior of solutions to
$$ \big(r^{\alpha}(u')^{p-1}\big)'=r^\alpha g(r)f(u), $$
0 less than r less than R, $u'(0)=0$, $u(r)\to\infty$ as $r\to R$.
The results obtained here generalize, and in some cases improve known results.

Submitted March 21, 2002. Published September 19, 2002.
Math Subject Classifications: 49K20, 34B15, 34C11, 35J65.
Key Words: Boundary behavior, blow-up solution, Keller-Osserman condition.

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Ahmed Mohammed
Department of Mathematical Sciences
Ball State University
Muncie, IN 47306, USA
e-mail: amohammed@bsu.edu

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