A Boundary Value Problem for Second Order Nonlinear Difference Equations on the Semi-infinite Interval

2002 ◽  
Vol 8 (11) ◽  
pp. 1019-1032 ◽  
Author(s):  
G.Sh. Guseinov
Keyword(s):  
Boundary Value Problem ◽  
Difference Equations ◽  
Boundary Value ◽  
Second Order ◽  
Infinite Interval ◽  
Nonlinear Difference Equations

scholarly journals A boundary value problem for second-order nonlinear difference equations on the integers

2005 ◽  
Vol 47 (2) ◽  
pp. 237-248
Author(s):  
F. Dal ◽  
G. Sh. Guseinov
Keyword(s):  
Boundary Value Problem ◽  
Difference Equations ◽  
Boundary Value ◽  
Second Order ◽  
Nonlinear Difference Equations ◽  
Left Hand ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Limit Circle Case ◽  
Difference Expression

AbstractIn this study, we are concerned with a boundary value problem (BVP) for nonlinear difference equations on the set of all integers Z. under the assumption that the left-hand side is a second-order linear difference expression which belongs to the so-called Weyl-Hamburger limit-circle case. The BVP is considered in the Hilbert space l2 and includes boundary conditions at infinity. Existence and uniqueness results for solution of the considered BVP are established.

scholarly journals On the Second-Order Quantum (p,q)-Difference Equations with Separated Boundary Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Chanon Promsakon ◽  
Nattapong Kamsrisuk ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Second Order ◽  
Uniqueness Of Solutions ◽  
Separated Boundary Conditions

In this paper, we investigate the existence and uniqueness of solutions for a boundary value problem for second-order quantum (p,q)-difference equations with separated boundary conditions, by using classical fixed point theorems. Examples illustrating the main results are also presented.

scholarly journals Existence of a positive solution for annth order boundary value problem for nonlinear difference equations

1997 ◽  
Vol 2 (3-4) ◽  
pp. 271-279 ◽  
Author(s):  
Johnny Henderson ◽  
Susan D. Lauer
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Point Theorem ◽  
Difference Equations ◽  
Boundary Value ◽  
Nonlinear Difference Equations

Thenth order eigenvalue problem:                                         Δnx(t)=(−1)n−kλf(t,x(t)),          t∈[0,T],x(0)=x(1)=⋯=x(k−1)=x(T+k+1)=⋯=x(T+n)=0,is considered, wheren≥2andk∈{1,2,…,n−1}are given. Eigenvaluesλare determined forfcontinuous and the case where the limitsf0(t)=limn→0+f(t,u)uandf∞(t)=limn→∞f(t,u)uexist for allt∈[0,T]. Guo's fixed point theorem is applied to operators defined on annular regions in a cone.

Existence and nonexistence of positive solutions to a discrete boundary value problem

2017 ◽  
Vol 33 (2) ◽  
pp. 181-190
Author(s):  
JOHNNY HENDERSON ◽  
◽  
RODICA LUCA ◽  
ALEXANDRU TUDORACHE ◽  
◽  
...  
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Difference Equations ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary ◽  
Order Difference ◽  
Discrete Boundary Value Problem ◽  
Existence And Nonexistence

We study the existence and nonexistence of positive solutions for a system of nonlinear second-order difference equations subject to coupled multi-point boundary conditions which contain some positive constants.

scholarly journals Solvability of a Class of Generalized Neumann Boundary Value Problems for Second-Order Nonlinear Difference Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Jianye Xia ◽  
Yuji Liu
Keyword(s):  
Boundary Value Problems ◽  
Difference Equations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Second Order ◽  
Nonlinear Difference Equations ◽  
Neumann Boundary Value Problems

This paper is motivated by Rachnkovab and Tisdell (2006) and Anderson et al. (2007). New sufficient conditions for the existence of at least one solution of the generalized Neumann boundary value problems for second order nonlinear difference equations∇Δx(k)=f(k,x(k),x(k+1)),k∈[1,n−1],x(0)=ax(1),x(n)=bx(n−1), are established.

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