scholarly journals POSITIVE SOLUTIONS OF THE SEMIPOSITONE NEUMANN BOUNDARY VALUE PROBLEM

2015 ◽  
Vol 20 (5) ◽  
pp. 578-584 ◽  
Author(s):  
Johnny Henderson ◽  
Nickolai Kosmatov
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Neumann Boundary Value Problem ◽  
At Resonance ◽  
Krasnoselskii Fixed Point Theorem ◽  
Problem At Resonance

In this paper we consider the Neumann boundary value problem at resonance −u''(t) = f t, u(t) , 0 < t < 1, u' (0) = u' (1) = 0. We assume that the nonlinear term satisfies the inequality f(t, z) + α2z + β(t) ≥ 0, t ∈ [0, 1], z ≥ 0, where β : [0, 1] → R + , and α ≠ 0. The problem is transformed into a non-resonant positone problem and positive solutions are obtained by means of a Guo–Krasnoselskii fixed point theorem.

On the Solvability of a Neumann Boundary Value Problem at Resonance

1997 ◽  
Vol 40 (4) ◽  
pp. 464-470 ◽  
Author(s):  
Chung-Cheng Kuo
Keyword(s):  
Boundary Value Problem ◽  
Nonlinear Term ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Semilinear Equations ◽  
Neumann Boundary Value Problem ◽  
At Resonance ◽  
Problem At Resonance

AbstractWe study the existence of solutions of the semilinear equations (1) in which the non-linearity g may grow superlinearly in u in one of directions u → ∞ and u → −∞, and (2) −Δu + g(x, u) = h, in which the nonlinear term g may grow superlinearly in u as |u| → ∞. The purpose of this paper is to obtain solvability theorems for (1) and (2) when the Landesman-Lazer condition does not hold. More precisely, we require that h may satisfy are arbitrarily nonnegative constants, . The proofs are based upon degree theoretic arguments.

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 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 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.

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