scholarly journals Green’s Function and Positive Solutions of a Third-Order Equation with Periodic Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Nickolai Kosmatov
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Periodic Boundary ◽  
Order Differential Equation ◽  
Periodic Boundary Conditions ◽  
Order Equation ◽  
Point Index ◽  
Third Order

We apply the fixed point index to obtain positive solutions of a nonresonant periodic boundary value problem for a third-order differential equation u‴+ρ3u=λfu.

Existence of positive solutions to multi-point third order problems with sign changing nonlinearities

2020 ◽  
Vol 24 (1) ◽  
pp. 109-129
Author(s):  
Abdulkadir Dogan ◽  
John R. Graef
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Point Index ◽  
Third Order ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions

In this paper, the authors examine the existence of positive solutions to a third-order boundary value problem having a sign changing nonlinearity. The proof makes use of fixed point index theory. An example is included to illustrate the applicability of the results.

scholarly journals Positive Solutions for a Hadamard Fractional p-Laplacian Three-Point Boundary Value Problem

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 439 ◽  
Author(s):  
Jiqiang Jiang ◽  
Donal O’Regan ◽  
Jiafa Xu ◽  
Yujun Cui
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Point Boundary ◽  
Point Index ◽  
Existence Of Positive Solutions ◽  
Increasing Operator

This article is to study a three-point boundary value problem of Hadamard fractional p-Laplacian differential equation. When our nonlinearity grows ( p − 1 ) -superlinearly and ( p − 1 ) -sublinearly, the existence of positive solutions is obtained via fixed point index. Moreover, using an increasing operator fixed-point theorem, the uniqueness of positive solutions and uniform convergence sequences are also established.

scholarly journals Existence and Lyapunov Stability of Positive Periodic Solutions for a Third-Order Neutral Differential Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-28 ◽  
Author(s):  
Jingli Ren ◽  
Zhibo Cheng ◽  
Yueli Chen
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Lyapunov Stability ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Neutral Differential Equation ◽  
Positive Periodic Solutions ◽  
Third Order

By applying Green's function of third-order differential equation and a fixed point theorem in cones, we obtain some sufficient conditions for existence, nonexistence, multiplicity, and Lyapunov stability of positive periodic solutions for a third-order neutral differential equation.

scholarly journals Positive Solutions for a System of Hadamard-Type Fractional Differential Equations with Semipositone Nonlinearities

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Youzheng Ding ◽  
Jiqiang Jiang ◽  
Donal O’Regan ◽  
Jiafa Xu
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Fixed Point Index ◽  
Nonnegative Matrices ◽  
Point Index ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

In this paper, we use the fixed-point index and nonnegative matrices to study the existence of positive solutions for a system of Hadamard-type fractional differential equations with semipositone nonlinearities.

scholarly journals Positive Solutions for a Class of Third-Order Three-Point Boundary Value Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Xiaojie Lin ◽  
Zhengmin Fu
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Positive Parameter ◽  
Point Boundary ◽  
Point Index ◽  
Third Order ◽  
Index Theorems ◽  
Existence Of Positive Solutions

We investigate the problem of existence of positive solutions for the nonlinear third-order three-point boundary value problemu‴(t)+λa(t)f(u(t))=0,0<t<1,u(0)=u′(0)=0,u″(1)=∝u″(η), whereλis a positive parameter,∝∈(0,1),η∈(0,1),f:(0,∞)→(0,∞),a:(0,1)→(0,∞)are continuous. Using a specially constructed cone, the fixed point index theorems and Leray-Schauder degree, this work shows the existence and multiplicities of positive solutions for the nonlinear third-order boundary value problem. Some examples are given to demonstrate the main results.

scholarly journals Positive solutions of three-point boundary value problems for higher-orderp-Laplacian with infinitely many singularities

2006 ◽  
Vol 2006 ◽  
pp. 1-12 ◽  
Author(s):  
Fuyi Xu ◽  
Yonghong Wu ◽  
Lishan Liu ◽  
Yunming Zhou
Keyword(s):  
Fixed Point ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Index Theorem ◽  
Point Boundary ◽  
Point Index ◽  
Fixed Point Index Theorem ◽  
Infinitely Many Singularities

We study a three-point nonlinear boundary value problem with higher-orderp-Laplacian. We show that there exist countable many positive solutions by using the fixed point index theorem for operators in a cone.

scholarly journals Eigenvalue of Coupled Systems for Hammerstein Integral Equation with Two Parameters

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Wanjun Li
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Index Theory ◽  
Coupled Systems ◽  
Point Index ◽  
Hammerstein Integral Equation ◽  
Fixed Point Index Theory ◽  
Two Parameters

By using the fixed-point index theory, we discuss the existence, multiplicity, and nonexistence of positive solutions for the coupled systems of Hammerstein integral equation with parameters.

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