Electron. J. Diff. Eqns., Vol. 2004(2004), No. 33, pp. 1-8.

Integrability of blow-up solutions to some non-linear differential equations

Michael Karls & Ahmed Mohammed

Abstract:
We investigate the integrability of solutions to the boundary blow-up problem
$$ r^{-\lambda}\bigl(r^{\lambda}(u')^{p-1}\bigr)'=H(r,u),\quad u'(0)\geq 0,\quad u(R)=\infty $$
under some appropriate conditions on the non-linearity $H$.

Submitted December 25, 2003. Published March 8, 2004.
Math Subject Classifications: 34C11, 34B15, 35J65.
Key Words: Blow-up solution, Keller-Osserman condition, integrability.

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Michael Karls
Department of Mathematical Sciences
Ball State University
Muncie, IN 47306, USA
email: mkarls@bsu.edu
Ahmed Mohammed
Department of Mathematical Sciences
Ball State University
Muncie, IN 47306, USA
email: amohammed@bsu.edu

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