Results 21 to 30 of about 745 (118)
Combinatorics of Matrix Factorizations and Integrable Systems [PDF]
, 2013 We study relations between the eigenvectors of rational matrix functions on the Riemann sphere. Our main result is that for a subclass of functions that are products of two elementary blocks it is possible to represent these relations in a combinatorial ...
Dzhamay, Anton
core +1 more source
Nonlinear Volterra difference equations in space lp
Discrete Dynamics in Nature and Society, Volume 2004, Issue 2, Page 301-306, 2004., 2004 We consider a class of vector nonlinear discrete‐time Volterra equations in space lp and derive estimates for the norms of solutions. These estimates give us explicit stability conditions, which allow us to avoid finding Lyapunov functionals.
Michael I. Gil′, Rigoberto Medina
wiley +1 more source
Fixed Points of Meromorphic Functions and Their Higher Order Differences and Shifts
Open Mathematics, 2019 In this paper, we investigate the relationships between fixed points of meromorphic functions, and their higher order differences and shifts, and generalize the case of fixed points into the more general case for first order difference and shift ...
Chen Hai-Ying, Zheng Xiu-Min
doaj +1 more source
Subdominant positive solutions of the discrete equation Δu(k + n) = −p(k)u(k)
Abstract and Applied Analysis, Volume 2004, Issue 6, Page 461-470, 2004., 2004 A delayed discrete equation Δu(k + n) = −p(k)u(k) with positive coefficient p is considered. Sufficient conditions with respect to p are formulated in order to guarantee the existence of positive solutions if k → ∞. As a tool of the proof of corresponding result, the method described in the author′s previous papers is used.
Jaromír Baštinec, Josef Diblík
wiley +1 more source
Positive solutions for singular discrete boundary value problems
Abstract and Applied Analysis, Volume 2004, Issue 4, Page 271-283, 2004., 2004 We study the existence of zero‐convergent solutions for the second‐order nonlinear difference equation Δ(anΦp(Δxn)) = g(n, xn+1), where Φp(u) = |u|p−2u, p > 1,{an} is a positive real sequence for n ≥ 1, and g is a positive continuous function on ℕ × (0, u0), 0 < u0 ≤ ∞. The effects of singular nonlinearities and of the forcing term are treated as well.
Mariella Cecchi +2 more
wiley +1 more source
Symplectic difference systems: oscillation theory and hyperbolic Prüfer transformation
Abstract and Applied Analysis, Volume 2004, Issue 4, Page 285-294, 2004., 2004 We present basic methods of oscillation theory of symplectic difference systems (SDSs). A particular attention is devoted to the variational principle and to the transformation method. Hyperbolic Prüfer transformation for SDSs is established.
Ondřej Došlý
wiley +1 more source
$N$-Bright-Dark Soliton Solution to a Semi-Discrete Vector Nonlinear Schr\"odinger Equation [PDF]
, 2017 In this paper, a general bright-dark soliton solution in the form of Pfaffian is constructed for an integrable semi-discrete vector NLS equation via Hirota's bilinear method.
Feng, Bao-Feng, Ohta, Yasuhiro
core +4 more sources
Accurate solution estimates for nonlinear nonautonomous vector difference equations
Abstract and Applied Analysis, Volume 2004, Issue 7, Page 603-611, 2004., 2004 The paper deals with the vector discrete dynamical system xk+1 = Akxk + fk(xk). Thewell‐known result by Perron states that this system is asymptotically stable if Ak ≡ A = const is stable and fk(x)≡f˜(x)=o(‖x‖). Perron′s result gives no information about the size of the region of asymptotic stability and norms of solutions.
Rigoberto Medina, M. I. Gil′
wiley +1 more source
Open Mathematics, 2016 In this paper, we investigate the value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations, and obtain the results on the relations between the order of the solutions and the ...
Luo Li-Qin, Zheng Xiu-Min
doaj +1 more source
Uniqueness on entire functions and their nth order exact differences with two shared values
Open Mathematics, 2020 Let f(z) be an entire function of hyper order strictly less than 1. We prove that if f(z) and its nth exact difference Δcnf(z){\Delta }_{c}^{n}f(z) share 0 CM and 1 IM, then Δcnf(z)≡f(z){\Delta }_{c}^{n}f(z)\equiv f(z).
Chen Shengjiang, Xu Aizhu
doaj +1 more source