Existence of solution for impulsive differential equations with indefinite linear part
type: Item
instance of: scholarly article
title: Existence of solution for impulsive differential equations with indefinite linear part
zbMATH Open document ID: 1336.34046
author: Qi Wang
author: Wang Mei
published in: Applied Mathematics Letters
publication date: 2015-12-09T00:00:00Z
review text: The authors consider the impulsive boundary value problem \[ \begin{aligned} &-u''(t) = f(t,u(t)), \quad t \in [0,1]\setminus\{t_1,\ldots,t_m\},\\ &u(0) = u(1) = 0, \\ &u'(t_j+) = u'(t_j-) - I_j(u(t_j)), \quad j=1,\ldots,m, \end{aligned} \] where \(m \in N\), \(0 < t_1 < t_2 < \ldots < t_m < 1\), \(f\) is a Carathéodory function on \((0,1)\times \mathbb{R}\), \(I_j : \mathbb{R} \to \mathbb{R}\) are continuous functions. Using critical point theory (Saddle Point Theorem), the existence of at least one solution for the non-resonant case is proved.
reviewed by: Jan Tomeček
Mathematics Subject Classification ID: 34B37
Mathematics Subject Classification ID: 58E50
zbMATH DE Number: 6518555
zbMATH Keywords: impulsive differential equation
zbMATH Keywords: indefinite linear part
zbMATH Keywords: Dirichlet boundary conditions
zbMATH Keywords: saddle point theorem
zbMATH Keywords: impulses at fixed times
MaRDI profile type: Publication
full work available at URL: j.aml.2015.07.003
OpenAlex ID: W1193415722
cites work: Q3824725
cites work: Q5454925
cites work: Q3995625
cites work: Q4853771
cites work: Periodic boundary value problems for a class of second-order impulsive integro-differential equations in Banach spaces
cites work: Multiple positive solutions of Dirichlet boundary value problems for second order impulsive differential equations
cites work: APPLICATIONS OF VARIATIONAL METHODS TO BOUNDARY-VALUE PROBLEM FOR IMPULSIVE DIFFERENTIAL EQUATIONS
cites work: Variational approach to impulsive differential equations
cites work: Existence and multiplicity of solutions for some Dirichlet problems with impulsive effects
cites work: An application of variational methods to Dirichlet boundary value problem with impulses
cites work: Variational approach to impulsive differential equations with periodic boundary conditions
cites work: Periodic and homoclinic solutions generated by impulses
cites work: Existence and multiplicity of solutions for an impulsive boundary value problem with a parameter via critical point theory
cites work: Q2995041
cites work: Multiplicity of solutions for nonlinear second order impulsive differential equations with linear derivative dependence via variational methods
cites work: Existence of subharmonic solutions for a class of second-order \(p\)-Laplacian systems with impulsive effects
cites work: Existence of weak solutions for impulsive \(p\)-Laplacian problem with superlinear impulses
cites work: Subharmonic solutions with prescribed minimal periodic for a class of second-order impulsive functional differential equations
cites work: The existence of subharmonic solutions with prescribed minimal period for forced pendulum equations with impulses
cites work: Some results for impulsive problems via Morse theory
cites work: On superquadratic periodic systems with indefinite linear part
cites work: Q3749777
DOI: 10.1016/J.AML.2015.07.003
description: scientific article; zbMATH DE number 6518555