Asymptotic decay of solutions of a nonlinear second-order differential equation with deviating argument
The purpose of this paper concerns the study of the existence and the asymptotic behaviour of decreasing solutions of second order nonlinear functional differential equations. So results already known for ordinary differential equations, such as the Thomas-Fermi one, the Schrödinger- Persico one, or the ones arising in the law of angular momentum conservation with a time dependent field strength, are generalized in presence of a deviating argument. A section is devoted to sufficient conditions in order that the considered equation has: (i) positive decreasing (negative increasing) solutions, (ii) solutions approaching a nonzero limit as the time t tends towards infinity. This is obtained using techniques which involve a comparison with a suitable linear ordinary differential equation. Another section studies the existence of solutions approaching zero as \(t\to \infty\), via a topological approach. The proof of Theorem 3 gives an estimate of the rate of convergence to zero.
Schrödinger-Persico differential equation
second order nonlinear functional differential equations
scientific article; zbMATH DE number 4103542
scientific article