On the solutions of second order generalized difference equations
MMS Manuel, A Kılıçman, GBA Xavier… - Advances in Difference …, 2012 - Springer
Advances in Difference Equations, 2012•Springer
In this article, the authors discuss ℓ 2 (ℓ) and c 0 (ℓ) solutions of the second order
generalized difference equation Δ ℓ 2 u (k)+ f (k, u (k))= 0, k∈[a,∞), a> 0 and we prove the
condition for non existence of non-trivial solution where Δ ℓ u (k)= u (k+ ℓ)− u (k) for ℓ> 0.
Further we present some formulae and examples to find the values of finite and infinite
series in number theory as application of Δ ℓ. MSC: 39A12, 39A70, 47B39, 39B60.
generalized difference equation Δ ℓ 2 u (k)+ f (k, u (k))= 0, k∈[a,∞), a> 0 and we prove the
condition for non existence of non-trivial solution where Δ ℓ u (k)= u (k+ ℓ)− u (k) for ℓ> 0.
Further we present some formulae and examples to find the values of finite and infinite
series in number theory as application of Δ ℓ. MSC: 39A12, 39A70, 47B39, 39B60.
Abstract
In this article, the authors discuss and solutions of the second order generalized difference equation
Δ ℓ 2 u ( k ) + f ( k , u ( k ) ) = 0 , k ∈ [ a , ∞ ) , a > 0
and we prove the condition for non existence of non-trivial solution where for . Further we present some formulae and examples to find the values of finite and infinite series in number theory as application of .
MSC:39A12, 39A70, 47B39, 39B60.
Springer
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