scholarly journals On the symmetric positive solutions of nonlinear fourth order ordinary differential equations with four-point boundary value conditions: a fixed point theory approach

2020 ◽  
Vol 13 (06) ◽  
pp. 364-377
Author(s):  
Md. Asaduzzaman ◽  
Md. Zulfikar Ali
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Positive Solutions ◽  
Fourth Order ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Theory Approach ◽  
Point Boundary ◽  
Symmetric Positive Solutions

scholarly journals The Existence of Symmetric Positive Solutions of Fourth-Order Elastic Beam Equations

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 121 ◽  
Author(s):  
Münevver Tuz
Keyword(s):  
Fixed Point ◽  
Positive Solutions ◽  
Fourth Order ◽  
Eigenvalue Problems ◽  
Fixed Point Theory ◽  
Elastic Beam ◽  
Point Theory ◽  
Beam Equations ◽  
Symmetric Positive Solutions ◽  
Elastic Beam Equations

In this study, we consider the eigenvalue problems of fourth-order elastic beam equations. By using Avery and Peterson’s fixed point theory, we prove the existence of symmetric positive solutions for four-point boundary value problem (BVP). After this, we show that there is at least one positive solution by applying the fixed point theorem of Guo-Krasnosel’skii.

scholarly journals Impulsive integral equations in Banach spaces and applications

1992 ◽  
Vol 5 (2) ◽  
pp. 111-122 ◽  
Author(s):  
Dajun Guo
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Banach Spaces ◽  
Integral Equations ◽  
Fixed Point Theory ◽  
Existence Theorems ◽  
Impulsive Differential Equations ◽  
Point Theory ◽  
Fredholm Integral Equations ◽  
Point Boundary

In this paper, we first use the fixed point theory to prove two existence theorems of positive solutions for the impulsive Fredholm integral Equations in Banach spaces. And then, we offer some applications to the two-point boundary value problems for the second order impulsive differential equations in Banach spaces.

scholarly journals Symmetric Positive Solutions for Nonlinear Singular Fourth-Order Eigenvalue Problems with Nonlocal Boundary Condition

2010 ◽  
Vol 2010 ◽  
pp. 1-16
Author(s):  
Fuyi Xu ◽  
Jian Liu
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Fourth Order ◽  
Eigenvalue Problems ◽  
Fixed Point Theory ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Point Theory ◽  
Symmetric Positive Solution ◽  
Symmetric Positive Solutions

We investigate nonlinear singular fourth-order eigenvalue problems with nonlocal boundary conditionu(4)(t)-λh(t)f(t,u,u′′)=0,0<t<1,u(0)=u(1)=∫01a(s)u(s)ds,u′′(0)=u′′(1)=∫01b(s)u′′(s)ds, wherea,b∈L1[0,1],λ>0,hmay be singular att=0and/or1. Moreoverf(t,x,y)may also have singularity atx=0and/ory=0. By using fixed point theory in cones, an explicit interval forλis derived such that for anyλin this interval, the existence of at least one symmetric positive solution to the boundary value problem is guaranteed. Our results extend and improve many known results including singular and nonsingular cases. The associated Green's function for the above problem is also given.

scholarly journals Positive Solutions for Second-Order Singular Semipositone Differential Equations Involving Stieltjes Integral Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Jiqiang Jiang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solutions ◽  
Nonlinear Term ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Second Order ◽  
Stieltjes Integral ◽  
Integral Conditions ◽  
Existence Of Positive Solutions

By means of the fixed point theory in cones, we investigate the existence of positive solutions for the following second-order singular differential equations with a negatively perturbed term:−u′′(t)=λ[f(t,u(t))−q(t)],0<t<1,αu(0)−βu′(0)=∫01u(s)dξ(s),γu(1)+δu′(1)=∫01u(s)dη(s),whereλ>0is a parameter;f:(0,1)×(0,∞)→[0,∞)is continuous;f(t,x)may be singular att=0,t=1,andx=0, and the perturbed termq:(0,1)→[0,+∞)is Lebesgue integrable and may have finitely many singularities in(0,1), which implies that the nonlinear term may change sign.

scholarly journals Positive Solutions forp-Laplacian Fourth-Order Differential System with Integral Boundary Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Jiqiang Jiang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fourth Order ◽  
Fixed Point Theory ◽  
Integral Boundary Conditions ◽  
Point Theory ◽  
Integral Boundary ◽  
Value System ◽  
Existence Of Positive Solutions

This paper investigates the existence of positive solutions for a class of singularp-Laplacian fourth-order differential equations with integral boundary conditions. By using the fixed point theory in cones, explicit range forλandμis derived such that for anyλandμlie in their respective interval, the existence of at least one positive solution to the boundary value system is guaranteed.

scholarly journals Existence results of ψ-Hilfer integro-differential equations with fractional order in Banach space

2020 ◽  
Vol 19 (1) ◽  
pp. 171-192
Author(s):  
Mohammed A. Almalahi ◽  
Satish K. Panchal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Banach Fixed Point Theorem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Mönch Fixed Point Theorem

AbstractIn this article we present the existence and uniqueness results for fractional integro-differential equations with ψ-Hilfer fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Mönch fixed point theorem and the Banach fixed point theorem. Furthermore, we discuss Eα -Ulam-Hyers stability of the presented problem. Also, we use the generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness of the δ-approximate solution.

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