scholarly journals POSITIVE SOLUTIONS OF A SECOND-ORDER NEUMANN BOUNDARY VALUE PROBLEM WITH A PARAMETER

2012 ◽  
Vol 86 (2) ◽  
pp. 244-253 ◽  
Author(s):  
YANG-WEN ZHANG ◽  
HONG-XU LI
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Existence And Uniqueness Theorem ◽  
Neumann Boundary Value Problem ◽  
Image Position ◽  
Continuous Dependence Of Solutions

AbstractIn this paper, we consider the Neumann boundary value problem with a parameter λ∈(0,∞): By using fixed point theorems in a cone, we obtain some existence, multiplicity and nonexistence results for positive solutions in terms of different values of λ. We also prove an existence and uniqueness theorem and show the continuous dependence of solutions on the parameter λ.

scholarly journals Existence of Positive Solutions for Neumann Boundary Value Problem with a Variable Coefficient

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Dongming Yan ◽  
Qiang Zhang ◽  
Zhigang Pan
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Variable Coefficient ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Neumann Boundary Value Problem ◽  
Existence Of Positive Solutions

We consider the existence of positive solutions for the Neumann boundary value problemx′′(t)+m2(t)x(t)=f(t,x(t))+e(t),t∈(0,    1),x′(0)=0,x′(1)=0, wherem∈C([0,1],(0,+∞)),e∈C[0,1],andf:[0,1]×(0,+∞)→[0,+∞)is continuous. The theorem obtained is very general and complements previous known results.

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.

Existence of positive solutions for a Neumann boundary value problem on the half-line via coincidence degree

2019 ◽  
Vol 10 (4) ◽  
pp. 447-458
Author(s):  
S. Djafri ◽  
Toufik Moussaoui
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Measurable Function ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Neumann Boundary ◽  
Half Line ◽  
Neumann Boundary Value Problem ◽  
Existence Of Positive Solutions

AbstractIn this paper, we are interested in the study of the existence of positive solutions for the following nonlinear boundary value problem on the half-line:\left\{\begin{aligned} \displaystyle-u^{\prime\prime}(x)&\displaystyle=q(x)f(x% ,u,u^{\prime}),&&\displaystyle x\in(0,+\infty),\\ \displaystyle u^{\prime}(0)&\displaystyle=u^{\prime}(+\infty)=0,\end{aligned}\right.where {q:\mathbb{R^{+}}\rightarrow\mathbb{R^{+}}} is a positive measurable function such that {\int_{0}^{+\infty}q(x)\,dx=1} and {f:\mathbb{R}^{+}\times\mathbb{R}^{2}\rightarrow\mathbb{R}} is q-Carathéodory.

Existence of solutions in a singular biharmonic nonlinear problem

1993 ◽  
Vol 36 (3) ◽  
pp. 537-546 ◽  
Author(s):  
Gaston L. Hernandez ◽  
Y. Choi
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Nonlinear Problem ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Image Position

In this work we prove the existence and uniqueness of positive solutions of the nonlinear singular boundary value problemwhere 0<σ<1.Extensions of the above results to the case of Δ2u−f(x, u) = 0 with appropriate singularity built into f are also given.

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