Integrability of blow-up solutions to some non-linear differential equations. (English) Zbl 1050.34045

Karls, Michael; Mohammed, Ahmed

Electron. J. Differ. Equ. 2004, Paper No. 33, 8 p. (2004).

Summary: We investigate the integrability of solutions to the boundary blow-up problem \[ r^{-\lambda} \bigl(r^\lambda (u')^{p-1} \bigr)'=H(r,u),\quad u'(0)\geq 0,\;u(R)=\infty\text{ for }r\to R. \] under some appropriate conditions on the nonlinearity \(H\).

MSC:

34C11	Growth and boundedness of solutions to ordinary differential equations
34B15	Nonlinear boundary value problems for ordinary differential equations

Keywords:

Blow-up solution; Keller-Osserman condition; integrability