Positive solutions of nonlinear fourth order iterative differential equations with two-point and integral boundary conditions

2021 ◽  
Vol 8 (1) ◽  
pp. 297-306
Author(s):  
Bouzid Mansouri ◽  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fourth Order ◽  
Continuous Dependence ◽  
Sufficient Conditions ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Iterative Differential Equations

Abstract This paper provides sufficient conditions to guarantee the existence, uniqueness and continuous dependence of positive solutions of a nonlinear fourth order iterative differential equations with two-point and integral boundary conditions. The main arguments are based on the Schauder fixed point theorem to prove the existence of a positive solution. As an application, we given an example to illustrate the obtained results.

scholarly journals POSITIVE SOLUTIONS OF NTH-ORDER BOUNDARY VALUE PROBLEMS WITH INTEGRAL BOUNDARY CONDITIONS

2015 ◽  
Vol 20 (2) ◽  
pp. 188-204 ◽  
Author(s):  
Ilkay Yaslan Karaca ◽  
Fatma Tokmak Fen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Integral Boundary Conditions ◽  
Integral Boundary

In this paper, by using double fixed point theorem and a new fixed point theorem, some sufficient conditions for the existence of at least two and at least three positive solutions of an nth-order boundary value problem with integral boundary conditions are established, respectively. We also give two examples to illustrate our main results.

scholarly journals Positive Solutions for Systems of Nonlinear Higher Order Differential Equations with Integral Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Yaohong Li ◽  
Xiaoyan Zhang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
General Type ◽  
Integral Boundary Conditions ◽  
Higher Order ◽  
Integral Boundary ◽  
Higher Order Differential Equations

By constructing some general type conditions and using fixed point theorem of cone, this paper investigates the existence of at least one and at least two positive solutions for systems of nonlinear higher order differential equations with integral boundary conditions. As application, some examples are given.

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.

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