A class of second order nonlinear differential equations with delay depenging on the unknown function of the fromin the case where ∫0∞ ds/r(s) < ∞ is studied. Various classifications of their eventually positive...A class of second order nonlinear differential equations with delay depenging on the unknown function of the fromin the case where ∫0∞ ds/r(s) < ∞ is studied. Various classifications of their eventually positive solutions are given in terms of their asymptotic magnitudes, and necessary as well as sufficient conditions for the existence of these solutions are also obtained.展开更多
In this paper, a class of second order nonlinear neutral difference equations with variable delays are studied. The criteria for existence of bounded eventually positive solution is obtained by using Banach contractio...In this paper, a class of second order nonlinear neutral difference equations with variable delays are studied. The criteria for existence of bounded eventually positive solution is obtained by using Banach contraction mapping principle and some necessary techniques. Moreover, some sufficient conditions for oscillation of the equations are given. Some results available in documents are extended in this paper. Illustrative examples are given.展开更多
In this paper,some new properties of solutions of the first order nonlinear differential inequalities with deviating arguments are given.These results improve many corresponding ones in the literature.
This paper is concerned with the existence of eventually positive solutions and oscillatory solutions of first-order neutral differential equation with positive and negative coefficients. The 'sharp' condition...This paper is concerned with the existence of eventually positive solutions and oscillatory solutions of first-order neutral differential equation with positive and negative coefficients. The 'sharp' conditions of oscillation for the equation have been obtained, i.e., the conditions are sufficient and necessary when all of the coefficients are constants. These conditions are distinguished from the previous criteria in the literatures, and also weaker than those existing results.展开更多
In this paper, a class of nonlinear difference equations are investigated. The sufficient conditions for the nonexistence of positive solutions are obtained. The results in this paper improve ones in [2].
We establish a new oscillation condition for even order neutral type differential equation of the following formwhere f is continuous and exists 1 ≤ k ≤ m(?)(t) ≡ Tk(t), a, (?)i ∈ C([0, ∞], R), i = 1, …,m. such ...We establish a new oscillation condition for even order neutral type differential equation of the following formwhere f is continuous and exists 1 ≤ k ≤ m(?)(t) ≡ Tk(t), a, (?)i ∈ C([0, ∞], R), i = 1, …,m. such that 0 ≤ a(t) ≤ L and展开更多
In this paper, new oscillation criteria are obtained for all solution of the firstorder neutral difference equation △(x(n) - P(n)x(n-m)) + Q(n)x(n-k) =0, n ≥n0 where m > 0, k≥ 0 are integers. p(n), Q(n)∈ C({n0...In this paper, new oscillation criteria are obtained for all solution of the firstorder neutral difference equation △(x(n) - P(n)x(n-m)) + Q(n)x(n-k) =0, n ≥n0 where m > 0, k≥ 0 are integers. p(n), Q(n)∈ C({n0, n0 + 1,...}, R+). Our results do not need the usual hypothesis ∑Q(s) = ∞. Some example are given s=N to demonstrate the advantage of our results than those in the literature.展开更多
文摘A class of second order nonlinear differential equations with delay depenging on the unknown function of the fromin the case where ∫0∞ ds/r(s) < ∞ is studied. Various classifications of their eventually positive solutions are given in terms of their asymptotic magnitudes, and necessary as well as sufficient conditions for the existence of these solutions are also obtained.
基金Supported by the Scientific Research Fund of Education Department of Hunan Province(07C680)
文摘In this paper, a class of second order nonlinear neutral difference equations with variable delays are studied. The criteria for existence of bounded eventually positive solution is obtained by using Banach contraction mapping principle and some necessary techniques. Moreover, some sufficient conditions for oscillation of the equations are given. Some results available in documents are extended in this paper. Illustrative examples are given.
文摘In this paper,some new properties of solutions of the first order nonlinear differential inequalities with deviating arguments are given.These results improve many corresponding ones in the literature.
基金Research supported by National Natural Science Foundation of P. R. China (10071016) by Foundation of the Education Department for Excellent Teacher of University.
文摘This paper is concerned with the existence of eventually positive solutions and oscillatory solutions of first-order neutral differential equation with positive and negative coefficients. The 'sharp' conditions of oscillation for the equation have been obtained, i.e., the conditions are sufficient and necessary when all of the coefficients are constants. These conditions are distinguished from the previous criteria in the literatures, and also weaker than those existing results.
文摘In this paper, a class of nonlinear difference equations are investigated. The sufficient conditions for the nonexistence of positive solutions are obtained. The results in this paper improve ones in [2].
基金This research is supported by NNSF of China(19875083,10275032).
文摘We establish a new oscillation condition for even order neutral type differential equation of the following formwhere f is continuous and exists 1 ≤ k ≤ m(?)(t) ≡ Tk(t), a, (?)i ∈ C([0, ∞], R), i = 1, …,m. such that 0 ≤ a(t) ≤ L and
文摘In this paper, new oscillation criteria are obtained for all solution of the firstorder neutral difference equation △(x(n) - P(n)x(n-m)) + Q(n)x(n-k) =0, n ≥n0 where m > 0, k≥ 0 are integers. p(n), Q(n)∈ C({n0, n0 + 1,...}, R+). Our results do not need the usual hypothesis ∑Q(s) = ∞. Some example are given s=N to demonstrate the advantage of our results than those in the literature.
