Nonexistence and Existence Results for a Fourth-Order p-Laplacian Discrete Neumann Boundary Value Problem

2015 ◽  
Vol 39 (1) ◽  
pp. 87-101 ◽  
Author(s):  
Xia Liu ◽  
Yuanbiao Zhang ◽  
Xiaoqing Deng
Keyword(s):  
Boundary Value Problem ◽  
Fourth Order ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Existence Results ◽  
Neumann Boundary Value Problem ◽  
Nonexistence And Existence

Existence and nonexistence results for a fourth-order discrete neumann boundary value problem

2014 ◽  
Vol 51 (2) ◽  
pp. 186-200
Author(s):  
Xia Liu ◽  
Yuanbiao Zhang ◽  
Haiping Shi
Keyword(s):  
Boundary Value Problem ◽  
Fourth Order ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Point Theory ◽  
Nonlinear Difference Equation ◽  
Neumann Boundary Value Problem ◽  
Existence And Nonexistence ◽  
Nonexistence Of Solutions

In this paper, a fourth-order nonlinear difference equation is considered. By making use of the critical point theory, we establish various sets of sufficient conditions for the existence and nonexistence of solutions for Neumann boundary value problem and give some new results. Results obtained generalize and complement the existing ones.

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.

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