scholarly journals A second order differential equation with generalized Sturm-Liouville integral boundary conditions at resonance

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1437-1444 ◽  
Author(s):  
Zengji Du ◽  
Jian Yin
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Nonlinear Differential Equations ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Integral Boundary Conditions ◽  
Second Order ◽  
Integral Boundary ◽  
At Resonance ◽  
Sturm Liouville

By using Mawhin coincidence degree theory, we investigate the existence of solutions for a class of second order nonlinear differential equations with generalized Sturm-Liouville integral boundary conditions at resonance. The results extend some known conclusions of integral boundary value problem at resonance for nonlinear differential equations

scholarly journals Resonant Integral Boundary Value Problems for Caputo Fractional Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Wenjie Ma ◽  
Shuman Meng ◽  
Yujun Cui
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
At Resonance ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
Integral Boundary Value Problems

This paper deals with the following Caputo fractional differential equations with Riemann-Stieltjes integral boundary conditions Dc0+αut=ft,ut,u′t,u′′t,  t∈0,1,  u0=u′′0=0,  u1=∫01‍utdAt, where Dc0+α denotes the standard Caputo derivative, α∈(2,3]; ∫01x(t)dA(t) denotes the Riemann-Stieltjes integrals of x with respect to A. By mean of coincidence degree theory, we obtain the existence of solutions for the above fractional BVP at resonance. In the end, according to the main results, we give a typical example.

scholarly journals On the Generalization of a Solution for a Class of Integro-Differential Equations with Nonseparated Integral Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Yanyuan Xing ◽  
Feng Jiao ◽  
Fang Liu
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Degree Theory ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Main Work ◽  
Uniqueness Results ◽  
Type Integral

In this paper, the existence and uniqueness results of the generalization nonlinear fractional integro-differential equations with nonseparated type integral boundary conditions are investigated. A natural formula of solutions is derived and some new existence and uniqueness results are obtained under some conditions for this class of problems by using standard fixed point theorems and Leray–Schauder degree theory, which extend and supplement some known results. Some examples are discussed for the illustration of the main work.

scholarly journals Existence of Solutions for Singular Second-Order Ordinary Differential Equations with Periodic and Deviated Nonlocal Multipoint Boundary Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Ahmed M. A. El-Sayed ◽  
Fatma M. Gaafar
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Integral Boundary Conditions ◽  
Second Order ◽  
Integral Boundary ◽  
Multipoint Boundary ◽  
Multipoint Boundary Conditions ◽  
Nonlocal Integral Conditions ◽  
Periodic Integral

This paper studies the existence of continuous solutions for a class of nonlinear singular second-order ordinary differential equations subject to one of the following boundary conditions: periodic-deviated multipoint boundary conditions, periodic-integral boundary conditions, and periodic-nonlocal integral conditions in the Riemann-Stieltjes sense. An existence result based on the Schauder fixed point theorem and Leray-Schauder continuation principle is used to obtain at least one continuous solution for the singular second-order ordinary differential problems. Two examples are given to show the application of our results.

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