scholarly journals Sign-Changing Solutions for Discrete Second-Order Three-Point Boundary Value Problems

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Tieshan He ◽  
Wei Yang ◽  
Fengjian Yang
Keyword(s):  
Fixed Point Index ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Degree Theory ◽  
Index Theory ◽  
Second Order ◽  
Topological Degree Theory ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Sign Changing Solutions

We consider the second-order three-point discrete boundary value problem. By using the topological degree theory and the fixed point index theory, we provide sufficient conditions for the existence of sign-changing solutions, positive solutions, and negative solutions. As an application, an example is given to demonstrate our main results.

scholarly journals Neutral Operator and Neutral Differential Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-29 ◽  
Author(s):  
Jingli Ren ◽  
Zhibo Cheng ◽  
Stefan Siegmund
Keyword(s):  
Fixed Point Index ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Index Theory ◽  
Positive Periodic Solutions ◽  
Point Index ◽  
Second Order Differential Equations ◽  
Fixed Point Index Theory ◽  
Neutral Operator

In this paper, we discuss the properties of the neutral operator(Ax)(t)=x(t)−cx(t−δ(t)), and by applying coincidence degree theory and fixed point index theory, we obtain sufficient conditions for the existence, multiplicity, and nonexistence of (positive) periodic solutions to two kinds of second-order differential equations with the prescribed neutral operator.

scholarly journals Existence of Nontrivial Solutions and Sign-Changing Solutions for Nonlinear Dynamic Equations on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-22 ◽  
Author(s):  
Huiye Xu
Keyword(s):  
Boundary Value Problem ◽  
Time Scales ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Degree Theory ◽  
Index Theory ◽  
Nontrivial Solutions ◽  
Nonlinear Dynamic Equations ◽  
Fixed Point Index Theory ◽  
Sign Changing Solutions

By using the topological degree theory and the fixed point index theory, the existence of nontrivial solutions and sign-changing solutions for a class of boundary value problem on time scales is obtained. We should point out that the integral operator corresponding to above boundary value problem is not assumed to be a cone mapping.

scholarly journals Positive solutions of a discrete second-order boundary value problems with fully nonlinear term

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Liyun Jin ◽  
Hua Luo
Keyword(s):  
Positive Solutions ◽  
Fixed Point Index ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Index Theory ◽  
Second Order ◽  
Fully Nonlinear ◽  
Fixed Point Index Theory ◽  
Weaker Conditions ◽  
Lower Limits

Abstract In this paper, we mainly consider a kind of discrete second-order boundary value problem with fully nonlinear term. By using the fixed-point index theory, we obtain some existence results of positive solutions of this kind of problems. Instead of the upper and lower limits condition on f, we may only impose some weaker conditions on f.

scholarly journals Positive Solutions for a Class of Fourth-Order Boundary Value Problems in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
Jingjing Cai ◽  
Guilong Liu
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Positive Solutions ◽  
Fourth Order ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Existence And Nonexistence

Using a specially constructed cone and the fixed point index theory, this work shows existence and nonexistence results of positive solutions for fourth-order boundary value problem with two different parameters in Banach spaces.

scholarly journals Positive Periodic Solutions of Second-Order Differential Equations with Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Yongxiang Li
Keyword(s):  
Periodic Solutions ◽  
Fixed Point Index ◽  
Order Differential Equation ◽  
Index Theory ◽  
Existence Results ◽  
Second Order ◽  
Positive Periodic Solutions ◽  
Point Index ◽  
Second Order Differential Equations ◽  
Fixed Point Index Theory

The existence results of positiveω-periodic solutions are obtained for the second-order differential equation with delays−u″+a(t)=f(t,u(t−τ1),...,u(t−τn)), wherea∈C(ℝ,(0,∞))is aω-periodic function,f:ℝ×[0,∞)n→[0,∞)is a continuous function, which isω-periodic int, andτ1,τ2,...,τnare positive constants. Our discussion is based on the fixed point index theory in cones.

scholarly journals Application of Fixed-Point Index Theory for a Nonlinear Fractional Boundary Value Problem with an Advanced Argument

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Li Wu ◽  
Chuanzhi Bai
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Fractional Boundary Value Problem ◽  
Point Index ◽  
Advanced Argument ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions

In this paper, we investigate the existence of positive solutions of a class of fractional three-point boundary value problem with an advanced argument by using fixed-point index theory. Our results improve and extend some known results in the literature. Two examples are given to demonstrate the effectiveness of our results.

Existence, multiplicity and non-existence of positive solutions for two-point boundary-value problems with strong singularity

2010 ◽  
Vol 140 (6) ◽  
pp. 1187-1196
Author(s):  
Chan-Gyun Kim
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Point Boundary ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions ◽  
Image Position

We study the existence, multiplicity and non-existence of positive solutions for the singular two-point boundary-value problemswhere $\varphi_{p}(s)=|s|^{p-2}s$, $p>1$, λ is a non-negative real parameter and f ∈ C((0, 1) × [0,∞), (0,∞)). Here, f(t, u) may be singular at t = 0 and/or 1. To obtain the main results we use the global continuation theorem and fixed-point index theory.

scholarly journals Positive solutions of singular nonlinear Sturm-Liouville boundary value problems

2004 ◽  
Vol 45 (4) ◽  
pp. 557-571
Author(s):  
Yan Sun ◽  
Lishan Liu ◽  
Yeol Je Cho
Keyword(s):  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Index Theory ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Point Index ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions ◽  
Sturm Liouville

AbstractBy using fixed point index theory, we present the existence of positive solutions for a Sturm-Liouville singular boundary value problem with at least one positive solution. Our results significantly extend and improve many known results even for non-singular cases.

scholarly journals Positive Periodic Solutions for Second-Order Ordinary Differential Equations with Derivative Terms and Singularity in Nonlinearities

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Yongxiang Li ◽  
Xiaoyu Jiang
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Fixed Point Index ◽  
Index Theory ◽  
Existence Results ◽  
Second Order ◽  
Positive Periodic Solutions ◽  
Point Index ◽  
Order Ordinary Differential Equation ◽  
Fixed Point Index Theory

The existence results of positiveω-periodic solutions are obtained for the second-order ordinary differential equationu′′(t)=f(t,u(t),u'(t)),t∈ℝwhere,f:ℝ×(0,∞)×ℝ→ℝis a continuous function, which isω-periodic intandf(t,u,v)may be singular atu=0. The discussion is based on the fixed point index theory in cones.

scholarly journals On Six Solutions form-Point Differential Equations System with Two Coupled Parallel Sub-Super Solutions

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Jian Liu ◽  
Hua Su ◽  
Shuli Wang
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Point Index ◽  
Index Theory ◽  
Second Order ◽  
Point Index ◽  
Fixed Point Index Theory

Under the assumption of two coupled parallel subsuper solutions, the existence of at least six solutions for a kind of second-orderm-point differential equations system is obtained using the fixed point index theory. As an application, an example to demonstrate our result is given.

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