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

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
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