Continuability and boundedness of solutions to nonlinear second-order differential equations

Abstract

Continuability, boundedness, and monotonicity of solutions for a class of second-order nonlinear differential equations are discussed. It is proved that all solutions are eventually monotonic and can be extended to infinity under some natural assumptions. Moreover, necessary and sufficient conditions for boundedness of all solutions are established. The results obtained have extended and improved some analogous existing ones.

Keywords

• Nonlinear differential equations
• second order
• boundedness
• monotonicity
• continuability
• asymptotic properties