q‐regular variation and the existence of solutions of half‐linear q‐difference equation
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DOI: 10.1002/mma.7570
Abstract: The half‐linear q‐difference equation Dq(p(t)Φ(Dq(x(t))))+r(t)Φ(x(qt))=0,t∈qℕ0={qn:n∈ℕ0},q>1, where Φ(x)=|x|αsgnx , α>0,p:qℕ0→(0,∞),r:qℕ0→ℝ , is analyzed in the framework of q‐regular variation. Necessary and sufficient conditions for the existence of q‐regularly varying solutions are given, under the assumption that… read more here.
Keywords: regular variation; half linear; linear difference; difference equation ... See more keywords
On Ulam stability of a third order linear difference equation in Banach spaces
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DOI: 10.1007/s00010-020-00722-5
Abstract: We obtain a result on Ulam stability and on the best Ulam constant for the linear difference equation $$x_{n+3}=ax_{n+2}+bx_{n+1}+c x_n,$$$$a,b,c \in \mathbb {K}$$, where $$\mathbb {K}$$ is one of the fields $$\mathbb {R}$$ or $$\mathbb… read more here.
Keywords: difference equation; linear difference; ulam stability;
On the best Ulam constant of a first order linear difference equation in Banach spaces
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DOI: 10.1007/s10474-020-01098-3
Abstract: We obtain some results on Ulam stability for the linear difference equation $$x_{n+1}=a_nx_n+b_n,\, n\geq0$$ , in a Banach space X. If there exists $$\lim_{n\to\infty}|a_n|=\lambda$$ , then the equation is Ulam stable if and only if… read more here.
Keywords: linear difference; best ulam; difference equation; equation ... See more keywords
On Bounded Solutions of a Difference Equation with Jumps of the Operator Coefficient
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DOI: 10.1007/s10958-018-3685-4
Abstract: We study the problem of existence of unique bounded solution of a difference equation with variable operator coefficient in the finite-dimensional Banach space. read more here.
Keywords: operator coefficient; difference equation; bounded solutions;
Comment on “New method to obtain periodic solutions of period two and three of a rational difference equation” [Nonlinear Dyn 79:241–250]
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DOI: 10.1007/s11071-016-3293-0
Abstract: In this paper, we discuss the results of Elsayed (Nonlinear Dyn 79:241–250, 2015) for periodic solution of period two and three of rational difference equation. Also, we study the existence of periodic solutions of some… read more here.
Keywords: dyn 241; 241 250; nonlinear dyn; difference equation ... See more keywords
Global behavior of a rational second order difference equation
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DOI: 10.1007/s12190-019-01276-9
Abstract: In this paper, we solve the difference equation $$\begin{aligned} x_{n+1}=\frac{\alpha }{1-x_nx_{n-1}}, \quad n=0,1,\ldots , \end{aligned}$$ x n + 1 = α 1 - x n x n - 1 , n = 0 , 1… read more here.
Keywords: difference equation; global behavior; alpha frac; frac sqrt ... See more keywords
Boundedness properties of the generalized Todd's difference equation
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DOI: 10.1080/10236198.2019.1619711
Abstract: ABSTRACT We consider the third-order difference equation with and We show that if then there exist positive initial conditions such that the solutions are unbounded except for the case and read more here.
Keywords: boundedness properties; difference; generalized todd; difference equation ... See more keywords
On a Difference Equation Generated by Two “Close” Squares
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DOI: 10.1134/s1995080219010074
Abstract: We consider a set of two squares constructed for the primitive periods 1 and i and having four vertices on one straight line. In a neighborhood of this set, we study a four-element difference equation… read more here.
Keywords: equation generated; generated two; difference equation; two close ... See more keywords
Homoclinic Solutions for a Higher Orderϕc-Laplacian Difference Equation Containing Both Advance and Retardation
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DOI: 10.1155/2019/3624842
Abstract: We consider a 2mth-order nonlinear difference equation containing both advance and retardation withϕc-Laplacian. Using the critical point theory, some new and concrete criteria for the existence of homoclinic solutions with mixed nonlinearities are obtained. read more here.
Keywords: equation containing; order; homoclinic solutions; containing advance ... See more keywords
Periodic Solution for a Max-Type Fuzzy Difference Equation
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DOI: 10.1155/2020/3094391
Abstract: 'e paper is concerned with the dynamics behavior of positive solutions for the following max-type fuzzy difference equation system: xn+1 � max A/xn, A/xn− 1, xn− 2 ???? ????, n � 0, 1, 2, .… read more here.
Keywords: max type; difference; fuzzy difference; difference equation ... See more keywords
A sharp oscillation criterion for a difference equation with constant delay
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DOI: 10.1186/s13662-020-03016-x
Abstract: It is known that all solutions of the difference equation Δ x ( n ) + p ( n ) x ( n − k ) = 0 , n ≥ 0 , $$\Delta x(n)+p(n)x(n-k)=0,… read more here.
Keywords: sharp oscillation; difference; criterion difference; oscillation criterion ... See more keywords