Transformation techniques and positive solutions on a parameter for three-point impulsive differential equations
type: Item
instance of: scholarly article
title: Transformation techniques and positive solutions on a parameter for three-point impulsive differential equations
zbMATH Open document ID: 1390.34054
author: Xintao Gao
author: Meiling Li
author: Yunqing Wang
published in: Journal of Applied Mathematics and Computing
publication date: 2018-04-13T00:00:00Z
review text: The authors consider the three-point boundary value problem for ODE with impulses at fixed times \[ \begin{aligned} & u''(t) + \lambda h(t) f(u(t)) = 0, \quad t \in (0,1), \;t \neq t_k,\\ & u(t_k^+) - u(t_k) = d_k u(t_k), \quad k = 1,\ldots,n,\\ & u'(0) = 0, \quad u(1) = \alpha u(\eta), \end{aligned} \] where \(\lambda > 0\), \(h \in L^p([0,1])\), \(p \in [1,\infty]\), \(f\) is continuous and nonnegative, \(0< t_1 <\ldots < t_n < 1\), \(\alpha >0\), \(d_k > -1\). The authors transform the problem into a non-impulsive problem. Using the eigenvalue and fixed point theory they obtain sufficient conditions for the existence of a positive solution of the BVP according to the values of parameter \(\lambda\).
reviewed by: Jan Tomeček
Mathematics Subject Classification ID: 34B09
Mathematics Subject Classification ID: 34B37
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 6859501
zbMATH Keywords: positive solutions
zbMATH Keywords: impulsive differential equations
zbMATH Keywords: eigenvalue
zbMATH Keywords: three-point boundary problem
MaRDI profile type: Publication
full work available at URL: s12190-017-1089-0
OpenAlex ID: W2590113704
cites work: Q3995625
cites work: Q4853771
cites work: Q3445966
cites work: Periodic boundary value problem for the second order impulsive functional differential equations
cites work: Multiple nonnegative solutions for second order impulsive differential equations.
cites work: Boundary value problems for a class of impulsive functional equations
cites work: Impulsive boundary value problems with integral boundary conditions and one-dimensional \(p\)-Laplacian
cites work: Existence of positive solutions for multipoint boundary value problem on the half-line with impulses
cites work: Multiple positive solutions of impulsive nonlinear Fredholm integral equations and applications
cites work: Existence of solution of \(m\)-point boundary value problems of second-order differential systems with impulses
cites work: Multiplicity results using bifurcation techniques for a class of boundary value problems of impulsive differential equations
cites work: Positive periodic solutions of first-order delay differential equations with impulses
cites work: Positive solutions for nonlinear \(n\)th-order singular nonlocal boundary value problems
cites work: Infinite boundary value problems for \(n\)th-order nonlinear impulsive integro-differential equations in Banach spaces
cites work: Multiple positive solutions of multi-point boundary value problem for second-order impulsive differential equations
cites work: Existence of solutions of boundary value problems with integral boundary conditions for second-order impulsive integro-differential equations in Banach spaces
cites work: Existence of positive periodic solutions of impulsive functional differential equations with two parameters
cites work: Triple positive pseudo-symmetric solutions to a four-point boundary value problem with \(p\)-Laplacian
cites work: Method of upper and lower solutions for second-order impulsive integro-differential equations in a Banach space
cites work: Extremal solutions for \(n\)th-order impulsive integro-differential equations on the half-line in Banach spaces
cites work: Existence and multiplicity of solutions for some Dirichlet problems with impulsive effects
cites work: Multiplicity of solutions for nonlinear second order impulsive differential equations with linear derivative dependence via variational methods
cites work: APPLICATIONS OF VARIATIONAL METHODS TO BOUNDARY-VALUE PROBLEM FOR IMPULSIVE DIFFERENTIAL EQUATIONS
cites work: Transformation techniques and fixed point theories to establish the positive solutions of second order impulsive differential equations
cites work: Q3994493
DOI: 10.1007/S12190-017-1089-0
description: scientific article; zbMATH DE number 6859501