scholarly journals An eigenvalue problem for quadratic pencils of q-difference equations and its applications

2009 ◽  
Vol 22 (4) ◽  
pp. 521-527 ◽  
Author(s):  
Adil Huseynov ◽  
Elgiz Bairamov
Keyword(s):  
Eigenvalue Problem ◽  
Difference Equations ◽  
Quadratic Pencils

scholarly journals SPECTRAL ESTIMATES FOR A NONHOMOGENEOUS DIFFERENCE PROBLEM

2010 ◽  
Vol 12 (06) ◽  
pp. 1015-1029 ◽  
Author(s):  
ALEXANDRU KRISTÁLY ◽  
MIHAI MIHĂILESCU ◽  
VICENŢIU RĂDULESCU ◽  
STEPAN TERSIAN
Keyword(s):  
Eigenvalue Problem ◽  
Difference Equations ◽  
Difference Problem ◽  
Spectral Estimates

We study an eigenvalue problem in the framework of difference equations. We show that there exist two positive constants λ0and λ1verifying λ0≤ λ1such that any λ ∈ (0, λ0) is not an eigenvalue of the problem, while any λ ∈ [λ1, ∞) is an eigenvalue of the problem. Some estimates for λ0and λ1are also given.

On testing difference equations for the diatomic eigenvalue problem

1988 ◽  
Vol 9 (8) ◽  
pp. 844-850 ◽  
Author(s):  
Hafez Kobeissi ◽  
Majida Kobeissi ◽  
Ali El Hajj
Keyword(s):  
Eigenvalue Problem ◽  
Difference Equations

scholarly journals On positive solution to multi-point fractional h-sum eigenvalue problems for caputo fractional h-difference equations

Filomat ◽  
2018 ◽  
Vol 32 (8) ◽  
pp. 2933-2951
Author(s):  
Saowaluck Chasreechai ◽  
Jarunee Soontharanon ◽  
Thanin Sitthiwirattham
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Eigenvalue Problem ◽  
Difference Equation ◽  
Positive Solution ◽  
Point Theorem ◽  
Difference Equations ◽  
Eigenvalue Problems

In this article, we study the existence of at least one positive solution to a multi-point fractional h-sum eigenvalue problem for Caputo fractional h-difference equation, by using the Guo-Krasnoselskii?s fixed point theorem. Moreover, we present some examples to display the importance of these results.

scholarly journals A focal boundary value problem for difference equations

1993 ◽  
Vol 16 (1) ◽  
pp. 169-176
Author(s):  
Cathryn Denny ◽  
Darrel Hankerson
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Difference Equations ◽  
Focal Point ◽  
Boundary Value ◽  
Positive Eigenvalue

The eigenvalue problem in difference equations,(−1)n−kΔny(t)=λ∑i=0k−1pi(t)Δiy(t), withΔty(0)=0,0≤i≤k,Δk+iy(T+1)=0,0≤i<n−k, is examined. Under suitable conditions on the coefficientspi, it is shown that the smallest positive eigenvalue is a decreasing function ofT. As a consequence, results concerning the first focal point for the boundary value problem withλ=1are obtained.

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.

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