Monotone solutions of a class of second order nonlinear differential equations. (English) Zbl 0552.34053

The asymptotic behavior of the solutions of \([p(t)F(x(t))x'(t)]'=q(t)g(x(t))\) is studied. Some necessary and sufficient conditions for boundedness of the solutions and an asymptotic comparison theorem are established. Oscillatory solutions are excluded by the hypotheses. The proofs are constructive.
Reviewer: W.Ames


34E05 Asymptotic expansions of solutions to ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
34C11 Growth and boundedness of solutions to ordinary differential equations
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