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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
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