Continuability and boundedness of solutions to nonlinear second-order differential equations. (English) Zbl 1217.34057

The authors consider the second order nonlinear differential equation
\[ [p(t)h(x(t))f({x}'(t)){]}' = q(t)g(x(t)),\text{ }t \geq a. \tag{1} \]
Continuability, boundedness and monotonicity of solutions of (1) are discussed. It is shown that all solutions of (1) are eventually monotonic and can be extended to infinity under some natural assumptions. Finally, some necessary and sufficient conditions for the boundedness of all solutions of (1) are established.


34C11 Growth and boundedness of solutions to ordinary differential equations
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