Results 11 to 20 of about 83 (83)
Estimates for the norms of solutions of difference systems with several delays
We derive explicit stability conditions for time‐dependent difference equations with several delays in Cn (the set of n complex vectors) and estimates for the size of the solutions. The growth rates obtained here are not necessarily decay rates.
Rigoberto Medina
wiley +1 more source
Hypersymmetric functions and Pochhammers of 2 × 2 nonautonomous matrices
We introduce the hypersymmetric functions of 2 × 2 nonautonomous matrices and show that they are related, by simple expressions, to the Pochhammers (factorial polynomials) of these matrices. The hypersymmetric functions are generalizations of the associated elementary symmetric functions, and for a specific class of 2 × 2 matrices, having a high degree
A. F. Antippa
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On a difference equation with min‐max response
We investigate the global behavior of the (positive) solutions of the difference equation xn+1 = αn + F(xn, …, xn−k), n = 0, 1, …, where (αn) is a sequence of positive reals and F is a min‐max function in the sense introduced here. Our results extend several results obtained in the literature.
George L. Karakostas, Stevo Stević
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Oscillation of Second-Order Half-linear Retarded Difference Equations via a Canonical Transform
The aim of this paper is to investigate the second order half-linear retarded difference equation Δ(μ(n)(Δη(n))α)+δ(n)ηα(σ(n))=0\Delta \left( {\mu \left( n \right){{\left( {\Delta \eta \left( n \right)} \right)}^\alpha }} \right) + \delta \left( n \right)
Srinivasan R.+3 more
doaj +1 more source
The existence of positive periodic solutions for a delayed discrete predator‐prey model with Holling‐type‐III functional response N1(k+1)=N1(k)exp{b1(k)-a1(k)N1(k-[τ1])-α1(k)N1(k)N2(k)/(N12(k)+m2N22(k))}, N2(k+1)=N2(k)exp{-b2(k)+α2(k)N12(k-[τ2])/(N12(k-[τ2])+m2N22(k-[τ2]))} is established by using the coincidence degree theory.
Lin-Lin Wang, Wan-Tong Li
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Oscillation and Property B for Semi-Canonical Third-Order Advanced Difference Equations
In this paper, we present sufficient conditions for the third-order nonlinear advanced difference equations of the form Δ(a(n))Δ(b(n)Δy((n)))=p(n)f(y(σ(n)))\Delta \left( {a\left( n \right)} \right)\Delta \left( {b\left( n \right)\Delta y\left( {\left( n \
Chatzarakis G.E.+2 more
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Nonlinear Volterra difference equations in space lp
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
Subdominant positive solutions of the discrete equation Δu(k + n) = −p(k)u(k)
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
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Positive solutions for singular discrete boundary value problems
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
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
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