Abstract
In this paper, sufficient conditions for the existence of positive periodic solutions of the second-order difference equation Δ 2 u(t−1)= g ( t ) u μ ( t ) − h ( t ) u λ ( t ) +f(t),t∈Z, are established, where g,h:Z→[0,∞) and f:Z→R are T-periodic functions, λ,μ>0.MSC:34B15.
Highlights
1 Introduction The theory of nonlinear difference equations has been widely used to study discrete models appearing in many fields such as computer science, economics, neural network, ecology, and cybernetics; see, for example, [ ]
There have been many papers to study the existence of positive periodic solutions for second-order difference equations
We find that difference equations are closely related to differential equations in the sense that (i) a differential equation model is usually derived from a difference equation, and (ii) numerical solutions of a differential equation have to be obtained by discretizing the differential equation
Summary
The theory of nonlinear difference equations has been widely used to study discrete models appearing in many fields such as computer science, economics, neural network, ecology, and cybernetics; see, for example, [ ]. Sufficient conditions for the existence of positive periodic solutions of the second-order difference equation g(t) uμ(t) h(t) uλ(t) There have been many papers to study the existence of positive periodic solutions for second-order difference equations. There are few techniques for studying the existence of positive solutions of difference equations with singularity, and the results in the field are very rare; see [ – ].
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