scholarly journals Positive solutions of fourth-order problems with dependence on all derivatives in nonlinearity under Stieltjes integral boundary conditions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yuexiao Ma ◽  
Chenyang Yin ◽  
Guowei Zhang
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Fourth Order ◽  
Integral Boundary Conditions ◽  
Stieltjes Integral ◽  
Integral Boundary ◽  
Fourth Order Problems

scholarly journals Solvability of a Fourth-Order Boundary Value Problem with Integral Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hui Li ◽  
Libo Wang ◽  
Minghe Pei
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fourth Order ◽  
Order Differential Equation ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Fourth Order Differential Equation

We investigate the existence of solutions and positive solutions for a nonlinear fourth-order differential equation with integral boundary conditions of the formx(4)(t)=f(t,x(t),x′(t),x′′(t),x′′′(t)),t∈[0,1],x(0)=x′(1)=0,x′′(0)=∫01h(s,x(s),x′(s),x′′(s))ds,x′′′(1)=0, wheref∈C([0,1]×ℝ4),h∈C([0,1]×ℝ3). By using a fixed point theorem due to D. O'Regan, the existence of solutions and positive solutions for the previous boundary value problems is obtained. Meanwhile, as applications, some examples are given to illustrate our results.

scholarly journals Positive Solutions for Fourth-Order Nonlinear Differential Equation with Integral Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Qi Wang ◽  
Yanping Guo ◽  
Yude Ji
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Nonlinear Differential Equation ◽  
Positive Solutions ◽  
Fourth Order ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Order Nonlinear Differential Equation ◽  
Existence And Nonexistence

This paper investigates the existence and nonexistence of positive solutions for a class of fourth-order nonlinear differential equation with integral boundary conditions. The associated Green's function for the fourth-order boundary value problems is first given, and the arguments are based on Krasnoselskii's fixed point theorem for operators on a cone.

scholarly journals The positive solutions of fractional differential equation with Riemann-Stieltjes integral boundary conditions

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2383-2394
Author(s):  
Xiaohan Zhang ◽  
Xiping Liu ◽  
Mei Jia ◽  
Haoliang Chen
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Stieltjes Integral ◽  
Integral Boundary ◽  
Fractional Differential ◽  
Integral Boundary Value Problems ◽  
Ordered Banach Spaces

In this paper, we study a class of fractional differential equations with Riemann-Stieltjes integral boundary conditions. The existence and uniqueness of positive solutions for the boundary value problem are obtained via the use of fixed point theorems on cones in partially ordered Banach spaces. Many of the multi-point and integral boundary value problems studied previously studied are also included in our results.

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