Asymptotically linear solutions of differential equations via Lyapunov functions

TL;DR

This paper introduces a novel Lyapunov function-based method to establish the existence of solutions with oblique asymptotes for certain nonlinear second-order differential equations, simplifying proofs for Emden-Fowler type equations.

Contribution

It presents a new approach using Lyapunov functions to prove the existence of asymptotically linear solutions, offering simpler proofs in this area.

Findings

Established existence of solutions with oblique asymptotes for specific differential equations

Provided a new Lyapunov function-based proof technique

Simplified analysis of Emden-Fowler like equations

Abstract

We discuss the existence of solutions with oblique asymptotes to a class of second order nonlinear ordinary differential equations by means of Lyapunov functions. The approach is new in this field and allows for simpler proofs of general results regarding Emden-Fowler like equations.