Blow-up solutions of nonlinear differential equations. (English) Zbl 1094.34021
The paper concerns the saturated solutions to certain differential systems
\[ u''=f(u,v),\quad v''=g(u,v) \]
as well as to the differential equation
\[ (| u'|^{m-2}u')'=u^p, \] with \(m\geq2\) and \(p>m-1\). The global or local feature of a solution is established by inspecting its initial data. The asymptotic behavior of global solutions is discussed, and life span, blow-up rates, and blow-up constants of local solutions are estimated. If the real number \(p\) is a positive rational number, namely \(p=r/s\), where \((r,s)=1\) and \(s\) is odd, there are also considered not necessarily positive solutions \(u\) to the differential equation.
\[ u''=f(u,v),\quad v''=g(u,v) \]
as well as to the differential equation
\[ (| u'|^{m-2}u')'=u^p, \] with \(m\geq2\) and \(p>m-1\). The global or local feature of a solution is established by inspecting its initial data. The asymptotic behavior of global solutions is discussed, and life span, blow-up rates, and blow-up constants of local solutions are estimated. If the real number \(p\) is a positive rational number, namely \(p=r/s\), where \((r,s)=1\) and \(s\) is odd, there are also considered not necessarily positive solutions \(u\) to the differential equation.
Reviewer: Corneliu Ursescu (Iaşi)
MSC:
| 34C11 | Growth and boundedness of solutions to ordinary differential equations |
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