Remarks on asymptotically linear dynamical systems at resonance
type: Item
instance of: scholarly article
title: Remarks on asymptotically linear dynamical systems at resonance
zbMATH Open document ID: 0921.58054
author: Carlo Greco
published in: Ricerche di Matematica
publication date: 1999-09-30T00:00:00Z
review text: The aim of this paper is to prove the existence of a nontrivial solution of the following system of ordinary differential equations: (1) \(\ddot x+V''(x,t)=0\), where \(V=V(x,t)\in C^2(\mathbb{R}^N \times\mathbb{R}, \mathbb{R})\) is a \(T_0\)-periodic function with respect to the variable \(t\), provided that the function \(V_1(x,t): =V(x,t)-{1\over 2} (A_0(t)x,x)\), \(A_0(t)= V''(0,t)\) satisfies some suitable condition at zero. Existence of a nontrivial solution (different from zero) of (1) is based on Morse theory.
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 37D15
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 1293113
zbMATH Keywords: resonance condition
zbMATH Keywords: existence
zbMATH Keywords: Morse theory
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1293113