Multiple positive solutions of a singular Emden-Fowler type problem for second-order impulsive differential systems
type: Item
instance of: scholarly article
title: Multiple positive solutions of a singular Emden-Fowler type problem for second-order impulsive differential systems
zbMATH Open document ID: 1213.34047
DOI: 10.1155/2011/212980
author: Sumit K. Garg
published in: Boundary Value Problems
publication date: 2010-12-13T00:00:00Z
full work available at URL: https://eudml.org/doc/223513
review text: The authors consider the boundary value problem with impulses \[ \begin{aligned}&u''(t) + \lambda h_1(t)f(u(t),v(t)) = 0, \quad t \in (0,1), \;t\neq t_1,\\ &v''(t) + \mu h_2(t)g(u(v),v(t)) = 0, \quad t \in (0,1), \;t\neq t_1,\\ &\triangle u_{|t=t_1} = I_u(u(t_1)), \quad \triangle v_{|t=t_1} = I_v(v(t_1)),\\ &\triangle u'_{|t=t_1} = N_u(u(t_1)), \quad \triangle v'_{|t=t_1} = N_v(v(t_1)),\\ &u(0) = a \geq 0, \quad v(0) = b \geq 0, \quad u(1) = c \geq 0, \quad v(1) = d \geq 0 \end{aligned} \] where \(\lambda\), \(\mu>0\), \(f\), \(g\), \(I_u\), \(I_v\), \(N_u\), \(N_v\), \(h_i\) are continuous, \(h_i\) may have a singularity at \(t=0\) and/or \(t=1\). Sufficient conditions ensuring the existence of at least one positive solution as well as two positive solutions. The results are obtained via the lower and upper solutions technique and fixed point index theorems.
reviewed by: Jan Tomeček
Mathematics Subject Classification ID: 34B37
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5825758
zbMATH Keywords: system of differential equations
zbMATH Keywords: second order
zbMATH Keywords: impulses
zbMATH Keywords: lower and upper solutions method
zbMATH Keywords: fixed point index theorem
zbMATH Keywords: existence
zbMATH Keywords: positive solution
Wikidata QID: Q59253376
MaRDI profile type: Publication
OpenAlex ID: W2022804568
cites work: Periodic boundary value problems for second order impulsive differential systems
cites work: Existence of periodic solutions of nonlinear systems of differential equations with impulse effect
cites work: Multiple positive solutions of a singular Gelfand type problem for second-order impulsive differential systems
cites work: Existence of solution of \(m\)-point boundary value problems of second-order differential systems with impulses
cites work: Positive solutions of two-point boundary value problems for systems of nonlinear second-order singular and impulsive differential equations
cites work: Periodic solutions for second order impulsive differential systems
cites work: A multiplicity result of positive radial solutions for a multiparameter elliptic system on an exterior domain
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description: scientific article; zbMATH DE number 5825758