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 Existence of Multiple Positive Solutions for Even Order Multi-Point Boundary Value Problems

2007 ◽  
Vol 14 (4) ◽  
pp. 775-792
Author(s):  
Youyu Wang ◽  
Weigao Ge
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Multiple Positive Solutions ◽  
Point Boundary ◽  
Even Order

Abstract In this paper, we consider the existence of multiple positive solutions for the 2𝑛th order 𝑚-point boundary value problem: where (0,1), 0 < ξ 1 < ξ 2 < ⋯ < ξ 𝑚–2 < 1. Using the Leggett–Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The associated Green's function for the above problem is also given.

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 Solvability of a nonlinear general third order four point eigenvalue problem on time scales

2011 ◽  
Vol 20 (2) ◽  
pp. 171-182
Author(s):  
S. NAGESWARA RAO ◽  
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Time Scales ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Order Four

We consider the four point boundary value problem for third order nonlinear differential equation on time scales ... subject to the boundary conditions ... t1 ≤ t2 ≤ t3 ≤ σ 3 (t4), α > 0, β > 0. Values of the parameter λ are determined for which the boundary value problem has a positive solution by utilizing a fixed point theorem on cone.

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.

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 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 of a positive solution for annth order boundary value problem for nonlinear difference equations

1997 ◽  
Vol 2 (3-4) ◽  
pp. 271-279 ◽  
Author(s):  
Johnny Henderson ◽  
Susan D. Lauer
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Point Theorem ◽  
Difference Equations ◽  
Boundary Value ◽  
Nonlinear Difference Equations

Thenth order eigenvalue problem:                                         Δnx(t)=(−1)n−kλf(t,x(t)),          t∈[0,T],x(0)=x(1)=⋯=x(k−1)=x(T+k+1)=⋯=x(T+n)=0,is considered, wheren≥2andk∈{1,2,…,n−1}are given. Eigenvaluesλare determined forfcontinuous and the case where the limitsf0(t)=limn→0+f(t,u)uandf∞(t)=limn→∞f(t,u)uexist for allt∈[0,T]. Guo's fixed point theorem is applied to operators defined on annular regions in a cone.

scholarly journals Fixed point theorems via Generalized WF-Contractions with applications

SeMA Journal ◽  
2021 ◽  
Author(s):  
Rosana Rodríguez-López ◽  
Rakesh Tiwari
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary ◽  
New Class ◽  
Second Order Differential Equations ◽  
Fixed Point Result

AbstractThe aim of this paper is to introduce a new class of mixed contractions which allow to revise and generalize some results obtained in [6] by R. Gubran, W. M. Alfaqih and M. Imdad. We also provide an example corresponding to this class of mappings and show how the new fixed point result relates to the above-mentioned result in [6]. Further, we present an application to the solvability of a two-point boundary value problem for second order differential equations.

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.

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