scholarly journals Some Existence Results of Positive Solution to Second-Order Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Shuhong Li ◽  
Xiaoping Zhang ◽  
Yongping Sun
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Boundary Value ◽  
Main Tool ◽  
Existence Results ◽  
Functional Type ◽  
The Fixed Point Theorem ◽  
Cone Expansion And Compression

We study the existence of positive and monotone solution to the boundary value problemu′′(t)+f(t,u(t))=0,0⩽t⩽1,u(0)=ξu(1),u'(1)=ηu'(0), whereξ,η∈(0,1)∪(1,∞). The main tool is the fixed point theorem of cone expansion and compression of functional type by Avery, Henderson, and O’Regan. Finally, four examples are provided to demonstrate the availability of our main results.

Existence of Positive Solution for Multi-Point Sturm-Liouville Boundary Value Problem

2011 ◽  
Vol 50-51 ◽  
pp. 704-708
Author(s):  
Xian Rui Meng ◽  
Na Na Li ◽  
Yu Xia Tong
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Point Boundary ◽  
Sturm Liouville ◽  
The Fixed Point Theorem ◽  
Cone Expansion And Compression

Multi-point boundary value problem is studied in this paper. With the condition that nonlinear term is superlinear or sublinear, it is proved that there exists at least one positive solution to multi-point Sturm-Liouville boundary value problem by using the fixed-point theorem concerning cone expansion and compression of norm type.

scholarly journals Existence and Nonexistence of Positive Solutions for a Higher-Order Three-Point Boundary Value Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yongping Sun ◽  
Qian Sun ◽  
Xiaoping Zhang
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Higher Order ◽  
Existence Results ◽  
Functional Type ◽  
Point Boundary ◽  
Existence And Nonexistence ◽  
Cone Expansion And Compression

This paper is concerned with the existence and nonexistence of positive solutions for a nonlinear higher-order three-point boundary value problem. The existence results are obtained by applying a fixed point theorem of cone expansion and compression of functional type due to Avery, Henderson, and O’Regan.

scholarly journals Some New Existence Results of Positive Solutions to an Even-Order Boundary Value Problem on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Yanbin Sang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Results ◽  
Point Boundary ◽  
Even Order

We consider a high-order three-point boundary value problem. Firstly, some new existence results of at least one positive solution for a noneigenvalue problem and an eigenvalue problem are established. Our approach is based on the application of three different fixed point theorems, which have extended and improved the famous Guo-Krasnosel’skii fixed point theorem at different aspects. Secondly, some examples are included to illustrate our results.

scholarly journals Positive Solutions to a Second-Order Discrete Boundary Value Problem

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Xiaojie Lin ◽  
Wenbin Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solution ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Second Order ◽  
The Fixed Point Theorem

We are concerned with second-order discrete boundary value problems and obtain some sufficient conditions for the existence of at least one positive solution by using the fixed point theorem due to Krasnosel'skii on a cone.

scholarly journals Multiple Positive Solutions for Fractional Three-Point Boundary Value Problem with p-Laplacian Operator

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Dong Li ◽  
Yang Liu ◽  
Chunli Wang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Multiple Positive Solutions ◽  
Point Boundary ◽  
The Fixed Point Theorem

In this paper, we investigate the existence of multiple positive solutions or at least one positive solution for fractional three-point boundary value problem with p-Laplacian operator. Our approach relies on the fixed point theorem on cones. The results obtained in this paper essentially improve and generalize some well-known results.

scholarly journals Existence Results for a Fully Fourth-Order Boundary Value Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yongxiang Li ◽  
Qiuyan Liang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Fourier Analysis ◽  
Growth Condition ◽  
Fourth Order ◽  
Boundary Value ◽  
Existence Of Solution ◽  
Existence Results ◽  
Analysis Method

We discuss the existence of solution for the fully fourth-order boundary value problemu(4)=f(t,u,u′,u′′,u′′′),0≤t≤1,u(0)=u(1)=u′′(0)=u′′(1)=0. A growth condition onfguaranteeing the existence of solution is presented. The discussion is based on the Fourier analysis method and Leray-Schauder fixed point theorem.

scholarly journals Some remarks on a Neumann boundary value problem arising in fluid dynamics

2004 ◽  
Vol 45 (3) ◽  
pp. 327-332 ◽  
Author(s):  
Pedro J. Torres
Keyword(s):  
Fluid Dynamics ◽  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Uniform Bounds ◽  
Neumann Boundary Value Problem

AbstractIt is proved that the Neumann boundary value problem, which Mays and Norbury have recently connected with a certain fluid dynamics equation, has a positive solution for any positive value of a particular parameter. Uniform bounds for the solutions and symmetry on a given range of the parameter are also introduced. The proofs include Krasnoselskii's classical fixed-point theorem on cones of a Banach space and basic comparison techniques.

scholarly journals Existence of Positive Solution for the Eighth-Order Boundary Value Problem Using Classical Version of Leray–Schauder Alternative Fixed Point Theorem

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 129 ◽  
Author(s):  
Thenmozhi Shanmugam ◽  
Marudai Muthiah ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Eighth Order ◽  
Classical Version ◽  
Nonlinear Alternative

In this work, we investigate the existence of solutions for the particular type of the eighth-order boundary value problem. We prove our results using classical version of Leray–Schauder nonlinear alternative fixed point theorem. Also we produce a few examples to illustrate our results.

scholarly journals Positive Solutions for Sturm-Liouville Boundary Value Problems in a Banach Space

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Hua Su ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Condition ◽  
Multiple Positive Solutions ◽  
Sturm Liouville ◽  
The Fixed Point Theorem

We consider the existence of single and multiple positive solutions for a second-order Sturm-Liouville boundary value problem in a Banach space. The sufficient condition for the existence of positive solution is obtained by the fixed point theorem of strict set contraction operators in the frame of the ODE technique. Our results significantly extend and improve many known results including singular and nonsingular cases.

Sign in / Sign up

Export Citation Format

Share Document