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 Multiplicity of positive solutions for second order Sturm-Liouville boundary value problems

2016 ◽  
Vol 25 (2) ◽  
pp. 215-222
Author(s):  
K. R. PRASAD ◽  
◽  
N. SREEDHAR ◽  
L. T. WESEN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Multiple Positive Solutions ◽  
Sturm Liouville ◽  
Multiplicity Of Positive Solutions

In this paper, we develop criteria for the existence of multiple positive solutions for second order Sturm-Liouville boundary value problem, u 00 + k 2u + f(t, u) = 0, 0 ≤ t ≤ 1, au(0) − bu0 (0) = 0 and cu(1) + du0 (1) = 0, where k ∈ 0, π 2 is a constant, by an application of Avery–Henderson fixed point theorem.

Existence of positive solutions for second-order undamped Sturm–Liouville boundary value problems

2016 ◽  
Vol 09 (04) ◽  
pp. 1650089 ◽  
Author(s):  
K. R. Prasad ◽  
L. T. Wesen ◽  
N. Sreedhar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Multiple Positive Solutions ◽  
Second Order Differential Equations ◽  
Existence Of Positive Solutions ◽  
Sturm Liouville

In this paper, we consider the second-order differential equations of the form [Formula: see text] satisfying the Sturm–Liouville boundary conditions [Formula: see text] where [Formula: see text]. By an application of Avery–Henderson fixed point theorem, we establish conditions for the existence of multiple positive solutions to the boundary value problem.

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 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 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 Positive Solutions for Boundary Value Problem of Nonlinear Fractional -Difference Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Moustafa El-Shahed ◽  
Farah M. Al-Askar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equation ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Multiple Positive Solutions ◽  
Fractional Boundary Value Problem ◽  
Fractional Difference ◽  
Fractional Difference Equation

We investigate the existence of multiple positive solutions to the nonlinear -fractional boundary value problem , , by using a fixed point theorem in a cone.

scholarly journals Multiple Positive Solutions for a Fractional Boundary Value Problem with Fractional Integral Deviating Argument

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
A. Guezane-Lakoud ◽  
R. Khaldi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Point Theorem ◽  
Fractional Integral ◽  
Boundary Value ◽  
Multiple Positive Solutions ◽  
Fractional Boundary Value Problem ◽  
Deviating Argument

This work is devoted to the existence of positive solutions for a fractional boundary value problem with fractional integral deviating argument. The proofs of the main results are based on Guo-Krasnoselskii fixed point theorem and Avery and Peterson fixed point theorem. Two examples are given to illustrate the obtained results, ending the paper.

scholarly journals Some second-order three-point boundary value problem for discrete equations on the half-line

2008 ◽  
Vol 39 (4) ◽  
pp. 271-290
Author(s):  
Yu Tian ◽  
Weigao Gi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Multiple Positive Solutions ◽  
Point Boundary ◽  
Discrete Equations ◽  
The Fixed Point Theorem

In this paper, we study the existence of multiple positive solutions of boundary value problems for second-order three-point discrete equations   $$\left \{\begin{array}{l}\Delta^2 x(n-1) - p\Delta x(n-1) - qx(n-1) + f(n, x(n)) = 0, \quad n \in N_0 \\ x(0) = \alpha x(l), \quad x(\infty) = 0\end{array}\right. . $$ The proofs are based on the fixed point theorem in Fr\'echet space (see [7]).

scholarly journals Multiple Positive Solutions for Nonlinear Fractional Boundary Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Daliang Zhao ◽  
Yansheng Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Auxiliary Problem ◽  
Multiple Positive Solutions ◽  
Fractional Boundary Value Problem ◽  
Krasnoselskii’S Fixed Point Theorem

This paper is devoted to the existence of multiple positive solutions for fractional boundary value problemDC0+αu(t)=f(t,u(t),u′(t)),0<t<1,u(1)=u′(1)=u′′(0)=0, where2<α≤3is a real number,CD0+αis the Caputo fractional derivative, andf:[0,1]×[0,+∞)×R→[0,+∞)is continuous. Firstly, by constructing a special cone, applying Guo-Krasnoselskii’s fixed point theorem and Leggett-Williams fixed point theorem, some new existence criteria for fractional boundary value problem are established; secondly, by applying a new extension of Krasnoselskii’s fixed point theorem, a sufficient condition is obtained for the existence of multiple positive solutions to the considered boundary value problem from its auxiliary problem. Finally, as applications, some illustrative examples are presented to support the main results.

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