scholarly journals An Existence Result of Positive Solutions for Fully Second-Order Boundary Value Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Yongxiang Li ◽  
Yaya Shang
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Existence Result ◽  
Boundary Value ◽  
Second Order ◽  
Upper Solution ◽  
Superlinear Growth ◽  
Lower And Upper Solution

An existence result of positive solutions is obtained for the fully second-order boundary value problem  -u′′(t)=f(t,u(t),u′(t)),  t∈[0,1],  u(0)=u(1)=0,wheref:[0,1]×R+×R→Ris continuous. The nonlinearityf(t,x,y)may be sign-changing and superlinear growth onxandy. Our discussion is based on the method of lower and upper solution.

scholarly journals Infinite Boundary Value Problems for Second-Order Nonlinear Impulsive Differential Equations with Supremum

2010 ◽  
Vol 2010 ◽  
pp. 1-15
Author(s):  
Piao-Piao Shi ◽  
Wen-Xia Wang
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Solution Method ◽  
Boundary Value ◽  
Impulsive Differential Equations ◽  
Existence Results ◽  
Second Order ◽  
Comparison Result ◽  
Upper Solution ◽  
Lower And Upper Solution

We investigate the infinite boundary value problems for second-order impulsive differential equations with supremum by establishing a new comparison result and using the lower and upper solution method, and obtain the existence results for their maximal and minimal solutions.

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 Parameter Dependence of Positive Solutions for Second-Order Singular Neumann Boundary Value Problems with Impulsive Effects

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Xuemei Zhang
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Second Order ◽  
Impulsive Effects ◽  
Parameter Dependence ◽  
Neumann Boundary Value Problem ◽  
Neumann Boundary Value Problems

The author considers the Neumann boundary value problem-y′′t+Myt=λωtft,yt,  t∈J,    t≠tk,  -Δy′|t=tk=λIktk,ytk,   k=1,2,…,m,  y′(0)=y′(1)=0and establishes the dependence results of the solution on the parameterλ, which cover equations without impulsive effects and are compared with some recent results by Nieto and O’Regan.

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 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.

Positive solutions for singular second order three-point boundary value problems

2007 ◽  
Vol 66 (12) ◽  
pp. 2756-2766 ◽  
Author(s):  
Bingmei Liu ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary
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