Extremal solutions for a class of nonlinear differential equations

Kreith, Kurt

doi:10.1090/S0002-9939-1980-0567983-8

Extremal solutions for a class of nonlinear differential equations
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Proc. Amer. Math. Soc. 79 (1980), 415-421 Request permission

Abstract:

Positive solutions of ${y^{(n)}} \pm f(t,y) = 0$ are characterized as maximal or minimal depending on whether their asymptotic behavior is $O({t^{n - 1}})$ or $O(1)$, respectively. Necessary and sufficient conditions for the existence of such extremal solutions are established.

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