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.

scholarly journals Positive Solutions to Periodic Boundary Value Problems for Four-Order Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Huantao Zhu ◽  
Zhiguo Luo
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Multiple Positive Solutions ◽  
Periodic Boundary Value Problems

We apply fixed point theorem in a cone to obtain sufficient conditions for the existence of single and multiple positive solutions of periodic boundary value problems for a class of four-order differential equations.

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.

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 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 Blow-Up Solutions for a Singular Nonlinear Hadamard Fractional Boundary Value Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Imed Bachar ◽  
Said Mesloub
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Blow Up ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Fractional Boundary Value Problems

We consider singular nonlinear Hadamard fractional boundary value problems. Using properties of Green’s function and a fixed point theorem, we show that the problem has positive solutions which blow up. Finally, some examples are provided to explain the applications of the results.

scholarly journals POSITIVE SOLUTIONS OF NTH-ORDER BOUNDARY VALUE PROBLEMS WITH INTEGRAL BOUNDARY CONDITIONS

2015 ◽  
Vol 20 (2) ◽  
pp. 188-204 ◽  
Author(s):  
Ilkay Yaslan Karaca ◽  
Fatma Tokmak Fen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Integral Boundary Conditions ◽  
Integral Boundary

In this paper, by using double fixed point theorem and a new fixed point theorem, some sufficient conditions for the existence of at least two and at least three positive solutions of an nth-order boundary value problem with integral boundary conditions are established, respectively. We also give two examples to illustrate our main results.

scholarly journals Existence and Uniqueness of Positive Solutions for a Singular Fractional Three-Point Boundary Value Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
I. J. Cabrera ◽  
J. Harjani ◽  
K. B. Sadarangani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Boundary Value ◽  
Point Boundary ◽  
Ordered Metric Spaces ◽  
Liouville Derivative

We investigate the existence and uniqueness of positive solutions for the following singular fractional three-point boundary value problemD0+αu(t)+f(t,u(t))=0, 0<t<1, u(0)=u′(0)=u′′(0)=0,u′′(1)=βu′′(η), where3<α≤4,D0+αis the standard Riemann-Liouville derivative andf:(0,1]×[0,∞)→[0,∞)withlim t→0+f(t,·)=∞(i.e.,fis singular att=0). Our analysis relies on a fixed point theorem in partially ordered metric spaces.

scholarly journals Existence and Nonexistence of Positive Solutions for Fractional Three-Point Boundary Value Problems with a Parameter

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Yunhong Li ◽  
Weihua Jiang
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Boundary Value ◽  
Point Boundary ◽  
Existence And Nonexistence ◽  
Fractional Differential

In this work, we investigate the existence and nonexistence of positive solutions for p-Laplacian fractional differential equation with a parameter. On the basis of the properties of Green’s function and Guo-Krasnosel’skii fixed point theorem on cones, the existence and nonexistence of positive solutions are obtained for the boundary value problems. We also give some examples to illustrate the effectiveness of our main results.

scholarly journals EXISTENCE OF POSITIVE SOLUTIONS FOR SUPERLINEAR SEMIPOSITONE $m$-POINT BOUNDARY-VALUE PROBLEMS

2003 ◽  
Vol 46 (2) ◽  
pp. 279-292 ◽  
Author(s):  
Ruyun Ma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Positive Parameter ◽  
Point Boundary ◽  
Existence Of Positive Solutions ◽  
The Fixed Point Theorem

AbstractIn this paper we consider the existence of positive solutions to the boundary-value problems\begin{align*} (p(t)u')'-q(t)u+\lambda f(t,u)\amp=0,\quad r\ltt\ltR, \\[2pt] au(r)-bp(r)u'(r)\amp=\sum^{m-2}_{i=1}\alpha_iu(\xi_i), \\ cu(R)+dp(R)u'(R)\amp=\sum^{m-2}_{i=1}\beta_iu(\xi_i), \end{align*}where $\lambda$ is a positive parameter, $a,b,c,d\in[0,\infty)$, $\xi_i\in(r,R)$, $\alpha_i,\beta_i\in[0,\infty)$ (for $i\in\{1,\dots m-2\}$) are given constants satisfying some suitable conditions. Our results extend some of the existing literature on superlinear semipositone problems. The proofs are based on the fixed-point theorem in cones.AMS 2000 Mathematics subject classification: Primary 34B10, 34B18, 34B15

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