scholarly journals Existence of Positive Solutions for a Fourth-Order Periodic Boundary Value Problem

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Yongxiang Li
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Fixed Point Index ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Index Theory ◽  
Periodic Boundary Value Problem ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions

The existence results of positive solutions are obtained for the fourth-order periodic boundary value problemu(4)−βu′′+αu=f(t,u,u′′),0≤t≤1,u(i)(0)=u(i)(1),  i=0,1,2,3, wheref:[0,1]×R+×R→R+is continuous,α,β∈R,and satisfy0<α<((β/2)+2π2)2,β>−2π2,(α/π4)+(β/π2)+1>0. The discussion is based on the fixed point index theory in cones.

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 The Existence and Multiplicity of Positive Solutions for Second-Order Periodic Boundary Value Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Feng Wang ◽  
Fang Zhang ◽  
Fuli Wang
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Second Order ◽  
Periodic Boundary Value Problem ◽  
Point Index ◽  
Existence And Multiplicity ◽  
Multiplicity Of Positive Solutions

The existence and multiplicity of positive solutions are established for second-order periodic boundary value problem. Our results are based on the theory of a fixed point index for A-proper semilinear operators defined on cones due to Cremins. Our approach is different in essence from other papers and the main results of this paper are also new.

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 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 Solutions for (k,n−k) Conjugate Multipoint Boundary Value Problems in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Yulin Zhao
Keyword(s):  
Positive Solutions ◽  
Fixed Point Index ◽  
Real Banach Space ◽  
Boundary Value ◽  
Index Theory ◽  
Zero Element ◽  
Singular Boundary ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions ◽  
Multipoint Boundary Value Problems

By means of the fixed point index theory of strict-set contraction operator, we study the existence of positive solutions for the multipoint singular boundary value problem(-1)n-kun(t)=f(t,ut),0<t<1,n≥2,1≤k≤n-1,u(0)=∑i=1m-2‍aiu(ξi),u(i)(0)=u(j)(1)=θ,1≤i≤k−1,0≤j≤n−k−1in a real Banach spaceE, whereθis the zero element ofE,0<ξ1<ξ2<⋯<ξm-2<1,ai∈[0,+∞),i=1,2,…,m-2.As an application, we give two examples to demonstrate our results.

scholarly journals Positive Solutions for Two-Point Boundary Value Problems for Fourth-Order Differential Equations with Fully Nonlinear Terms

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Yixin Zhang ◽  
Yujun Cui
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Linear Operators ◽  
Continuous Space ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions

In this paper, we consider the existence of positive solutions for the fully fourth-order boundary value problem u 4 t = f t , u t , u ′ t , u ″ t , u ‴ t ,   0 ≤ t ≤ 1 , u 0 = u 1 = u ″ 0 = u ″ 1 = 0 , where f : 0,1 × 0 , + ∞ × − ∞ , + ∞ × − ∞ , 0 × − ∞ , + ∞ ⟶ 0 , + ∞ is continuous. This equation can simulate the deformation of an elastic beam simply supported at both ends in a balanced state. By using the fixed-point index theory and the cone theory, we discuss the existence of positive solutions of the fully fourth-order boundary value problem. We transform the fourth-order differential equation into a second-order differential equation by order reduction method. And then, we examine the spectral radius of linear operators and the equivalent norm on continuous space. After that, we obtain the existence of positive solutions of such BVP.

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