scholarly journals Positive solution of a system of integral equations with applications to boundary value problems of differential equations

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Chunfang Shen ◽  
Hui Zhou ◽  
Liu Yang
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solution ◽  
Integral Equations ◽  
Boundary Value ◽  
System Of Integral Equations

scholarly journals Aboodh and Mahgoub Transform in Boundary Value Problems of System of Ordinary Differential Equations

2021 ◽  
pp. 67-75
Author(s):  
Dr. D. P. Patil
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Integral Equations ◽  
Boundary Value ◽  
Integral Transforms

Integral transforms plays important role in solving differential equations and integral equations. In this paper we discuss application of Aboodh transform and Mahgoub transform in solving boundary value problem of system of ordinary differential equations and result shows that Aboodh transform and Mahgoub transform are closely connected.

scholarly journals New Lyapunov-type inequalities for fractional multi-point boundary value problems involving Hilfer-Katugampola fractional derivative

2021 ◽  
Vol 7 (1) ◽  
pp. 1074-1094
Author(s):  
Wei Zhang ◽  
◽  
Jifeng Zhang ◽  
Jinbo Ni
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Integral Equations ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Contraction Principle ◽  
Point Boundary ◽  
Fractional Differential ◽  
Banach’S Contraction Principle

<abstract><p>In this paper, we present new Lyapunov-type inequalities for Hilfer-Katugampola fractional differential equations. We first give some unique properties of the Hilfer-Katugampola fractional derivative, and then by using these new properties we convert the multi-point boundary value problems of Hilfer-Katugampola fractional differential equations into the equivalent integral equations with corresponding Green's functions, respectively. Finally, we make use of the Banach's contraction principle to derive the desired results, and give a series of corollaries to show that the current results extend and enrich the previous results in the literature.</p></abstract>

scholarly journals Eigenvalues of boundary value problems for higher order differential equations

1996 ◽  
Vol 2 (5) ◽  
pp. 401-434 ◽  
Author(s):  
Patricia J. Y. Wong ◽  
Ravi P. Agarwal
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solution ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Existence Of Positive Solutions ◽  
Alpha Beta ◽  
Special Case ◽  
Higher Order Differential Equations

We shall consider the boundary value problemy(n)+λQ(t,y,y1,⋅⋅⋅,y(n−2))=λP(t,y,y1,⋅⋅⋅,y(n−1)),n≥2,t∈(0,1),y(i)(0)=0,0≤i≤n−3,αy(n−2)(0)−βy(n−1)(0)=0,γy(n−2)(1)+δy(n−1)=0,whereλ>0,α,β,γandδare constants satisfyingαγ+αδ+βγ>0,β,δ≥0,β+α>0andδ+γ>0to characterize the values ofλso that it has a positive solution. For the special caseλ=1, sufficient conditions are also established for the existence of positive solutions.

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