scholarly journals Solution and positive solution for a semilinear third-order two-point boundary value problem

2004 ◽  
Vol 17 (10) ◽  
pp. 1171-1175 ◽  
Author(s):  
Qingliu Yao
Keyword(s):  
Boundary Value Problem ◽  
Positive Solution ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order

scholarly journals Iteration for a Third-Order Three-Point BVP with Sign-Changing Green's Function

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Ya-Hong Zhao ◽  
Xing-Long Li
Keyword(s):  
Iterative Method ◽  
Boundary Value Problem ◽  
Green’S Function ◽  
Positive Solution ◽  
Green's Function ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Monotone Positive Solution

We are concerned with the following third-order three-point boundary value problem:u‴(t)=f(t,u(t)),t∈[0,1],u′(0)=u(1)=0,u″(η)+αu(0)=0, whereα∈[0,2)andη∈[2/3,1). Although corresponding Green's function is sign-changing, we still obtain the existence of monotone positive solution under some suitable conditions onfby applying iterative method. An example is also included to illustrate the main results obtained.

scholarly journals POSITIVE SOLUTION FOR NONLINEAR THIRD-ORDER MULTI-POINT BOUNDARY VALUE PROBLEM AT RESONANCE

2020 ◽  
Vol 10 (3) ◽  
pp. 842-852
Author(s):  
Chunfang Shen ◽  
◽  
Hui Zhou ◽  
Xiaoxiang Fan ◽  
Liu Yang
Keyword(s):  
Boundary Value Problem ◽  
Positive Solution ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
At Resonance ◽  
Problem At Resonance

Positive Solution for Boundary Value Problem of Nonlinear Three-Order Difference Equation

2014 ◽  
Vol 926-930 ◽  
pp. 3665-3668
Author(s):  
Chun Li Wang ◽  
Chuan Zhi Bai ◽  
Xiao Dong Cai
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equation ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Order Difference ◽  
Order Difference Equation

In this paper we investigate the existence of positive solution of the following nonlinear discrete third-order two-point boundary value problem. whereis continuous and there existssuch that . Our approach relies on the Krasnosel'skii fixed point theorem. An example is given to demonstrate the application of the theorem obtained.

scholarly journals Positive Solution for the Integral and Infinite Point Boundary Value Problem for Fractional-Order Differential Equation Involving a Generalized ϕ-Laplacian Operator

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Nadir Benkaci-Ali
Keyword(s):  
Boundary Value Problem ◽  
Positive Solution ◽  
Fixed Point Index ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Point Boundary ◽  
Fractional Order Differential Equation ◽  
Infinite Point ◽  
Liouville Derivative

In this paper, we establish the existence of nontrivial positive solution to the following integral-infinite point boundary-value problem involving ϕ-Laplacian operator D0+αϕx,D0+βux+fx,ux=0,x∈0,1,D0+σu0=D0+βu0=0,u1=∫01 gtutdt+∑n=1n=+∞ αnuηn, where ϕ:0,1×R→R is a continuous function and D0+p is the Riemann-Liouville derivative for p∈α,β,σ. By using some properties of fixed point index, we obtain the existence results and give an example at last.

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