Comparison theorems for second order nonlinear difference equations
نویسندگان
چکیده
منابع مشابه
Oscillation theorems for second-order nonlinear delay difference equations
By means of Riccati transformation technique, we establish some new oscillation criteria for second-order nonlinear delay difference equation ∆(pn (∆xn) ) + qnf(xn−σ) = 0, n = 0, 1, 2, . . . ,
متن کاملOscillation Theorems for Second Order Nonlinear Neutral Type Difference Equations with Positive and Negative Coefficients
In this paper, the authors using two inequalities and Ricatti type transformation obtained some new oscillation results for the second order nonlinear neutral type difference equations of the form ∆(an∆(xn + cnxn−k)) + pnf(xn+1−l)− qng(xn+1−m) = 0, and ∆(an∆(xn − cnxn−k)) + pnf(xn+1−l)− qng(xn+1−m) = 0. The obtained results improve, extend and generalize some of the known results. Further examp...
متن کاملExistence Theorems of Periodic Solutions for Second-Order Nonlinear Difference Equations
In 1.1 , the given real sequences {pn}, {qn} satisfy pn T pn > 0, qn T qn for any n ∈ Z, f : Z×R → R is continuous in the second variable, and f n T, z f n, z for a given positive integer T and for all n, z ∈ Z×R. −1 δ −1, δ > 0, and δ is the ratio of odd positive integers. By a solution of 1.1 , we mean a real sequence x {xn}, n ∈ Z, satisfying 1.1 . In 1, 2 , the qualitative behavior of linea...
متن کاملOscillation Theorems for Second Order Nonlinear Differential Equations with Damping
Some oscillation criteria for solutions of a general ordinary differential equation of second order of the form (r(t)ψ(x(t))ẋ(t))+h(t)ẋ(t)+q(t)φ(g(x(t)),r(t)ψ(x(t))ẋ(t)) = H(t,x(t), ẋ(t)) with alternating coefficients are discussed. Our results improve and extend some existing results in the literature. Some illustrative examples are given with its numerical solutions which are computed using R...
متن کاملOscillation Theorems for Second-Order Damped Nonlinear Differential Equations
We present new oscillation criteria for the differential equation of the form r t U t ′ p t k2 x t , x′ t |x t |U t q t φ x g1 t , x′ g2 t f x t 0, where U t k1 x t , x′ t |x′ t |α−1x′ t , α ≤ β, ν β − α / α 1 . Our research is different from most known ones in the sense that H function is not employed in our results, though Riccati’s substitution and its generalized forms are used. Our criteri...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2005
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2004.12.024