The asymptotic behavior of solutions of nonlinear second-order difference equations
نویسندگان
چکیده
منابع مشابه
Asymptotic Behavior of Solutions of Nonlinear Difference Equations
The nonlinear difference equation (E) xn+1 − xn = anφn(xσ(n)) + bn, where (an), (bn) are real sequences, φn : −→ , (σ(n)) is a sequence of integers and lim n−→∞ σ(n) =∞, is investigated. Sufficient conditions for the existence of solutions of this equation asymptotically equivalent to the solutions of the equation yn+1 − yn = bn are given. Sufficient conditions under which for every real consta...
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The development of the study of periodic solution of functional difference equations is relatively rapid. There has been many approaches to study periodic solutions of difference equations, such as critical point theory, fixed point theorems in Banach spaces or in cones of Banach spaces, coincidence degree theory, KaplanYorke method, and so on, one may see [3-7,11,13-15] and the references ther...
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The two-dimensional system of nonlinear differential equations (A) x′′ = p(t)y, y′′ = q(t)x , with positive exponents α and β satisfying αβ < 1 is analyzed in the framework of regular variation. Under the assumption that p(t) and q(t) are nearly regularly varying it is shown that system (A) may possess three types of positive solutions (x(t), y(t)) which are strongly monotone in the sense that ...
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متن کاملPeriodic solutions for nonlinear second-order difference equations
We establish conditions for the existence of periodic solutions of nonlinear, second-order difference equations of the form y(t + 2) + by(t + 1) + cy(t) = f (y(t)), where c = 0 and f :R→ R is continuous. In our main result we assume that f exhibits sublinear growth and that there is a constant β > 0 such that u f (u) > 0 whenever |u| ≥ β. For such an equation we prove that ifN is an odd integer...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2001
ISSN: 0893-9659
DOI: 10.1016/s0893-9659(00)00202-0