Existence results for positive solutions to iterative systems of four-point fractional-order boundary value problems in a Banach space

2018 ◽  
Vol 13 (04) ◽  
pp. 2050070
Author(s):  
Kapula Rajendra Prasad ◽  
Boddu Muralee Bala Krushna ◽  
L. T. Wesen
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Fractional Order ◽  
Boundary Value ◽  
Existence Results ◽  
Iterative System ◽  
Iterative Systems ◽  
Eigenvalue Intervals

We investigate the eigenvalue intervals of [Formula: see text] for which the iterative system of four-point fractional-order boundary value problem has at least one positive solution by utilizing Guo–Krasnosel’skii fixed point theorem under suitable conditions. The obtained results in the paper are illustrated with an example for their feasibility.

Eigenvalues for iterative systems of Sturm-Liouville fractional order two-point boundary value problems

2014 ◽  
Vol 17 (3) ◽  
Author(s):  
Kapula Prasad ◽  
Boddu Krushna
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Fractional Order ◽  
Boundary Value ◽  
Point Boundary ◽  
Iterative System ◽  
Sturm Liouville ◽  
Iterative Systems ◽  
Eigenvalue Intervals

AbstractIn this paper, we determine the eigenvalue intervals of λ 1, λ 2, ..., λ n for which the iterative system of nonlinear Sturm-Liouville fractional order two-point boundary value problem possesses a positive solution by an application of Guo-Krasnosel’skii fixed point theorem on a cone.

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 three positive solutions for boundary value problem with fractional order and infinite delay

2015 ◽  
Vol 53 (1) ◽  
pp. 57-76
Author(s):  
Hedia Benaouda
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fractional Order ◽  
Point Theorem ◽  
Infinite Delay ◽  
Boundary Value

Abstract In this paper we investigate the existence three positives solutions by using Leggett-Williams fixed point theorem in cones for three boundary value problem with fractional order and infinite delay.

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 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.

scholarly journals Eigenvalue intervals for iterative systems of nonlinear boundary value problems on time scales

2013 ◽  
Vol 22 (1) ◽  
pp. 95-104
Author(s):  
SABBAVARAPU NAGESWARA RAO ◽  
◽  
ALLAKA KAMESWARA RAO ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Time Scale ◽  
Nonlinear Boundary ◽  
Dynamic Equations ◽  
Nonlinear Boundary Value Problems ◽  
Iterative System ◽  
Iterative Systems ◽  
Eigenvalue Intervals

Values of λ1, λ2, · · · , λn are determined for which there exist positive solutions of the iterative system of dynamic equations, u∆∆ i (t) + λiai(t)fi(ui+1(σ(t))) = 0, 1 ≤ i ≤ n, un+1(t) = u1(t), for t ∈ [a, b]T, and satisfying the boundary conditions, αui(a) − βu∆ i (a) = 0 = γui(σ 2 (b)) + δu∆ i (σ(b)), 1 ≤ i ≤ n, where T is a time scale. A Guo-Krasnosel’skii fixed point theorem is applied.

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.

L 1-solutions of the boundary value problem for implicit fractional order differential equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Benoumran Telli ◽  
Mohammed Said Souid
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Order ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Abstract The aim of this paper is to present new results on the existence of solutions for a class of the boundary value problem for fractional order implicit differential equations involving the Caputo fractional derivative. Our results are based on Schauder’s fixed point theorem and the Banach contraction principle fixed point theorem.

scholarly journals Existence of a unique positive solution for a singular fractional boundary value problem

2018 ◽  
Vol 34 (1) ◽  
pp. 57-64
Author(s):  
E. T. KARIMOV ◽  
◽  
K. SADARANGANI ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Positive Solution ◽  
Fractional Order ◽  
Boundary Value ◽  
Order Equation ◽  
Fractional Boundary Value Problem ◽  
Unique Positive Solution

In the present work, we discuss the existence of a unique positive solution of a boundary value problem for a nonlinear fractional order equation with singularity. Precisely, order of equation Dα 0+u(t) = f(t, u(t)) belongs to (3, 4] and f has a singularity at t = 0 and as a boundary conditions we use... Using a fixed point theorem, we prove the existence of unique positive solution of the considered problem.

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