We establish some new criteria for the oscillation of even order nonlinear dynamic equation. We study the case of strongly super-linear and the case of strongly sub-linear subject to various conditions.
This paper presents a strong subfeasible directions algorithm possessing superlinear convergence for inequality constrained optimization. The starting point of this algorithm may be arbitary and its feasibility is mon...This paper presents a strong subfeasible directions algorithm possessing superlinear convergence for inequality constrained optimization. The starting point of this algorithm may be arbitary and its feasibility is monotonically increasing. The search directions only depend on solving one quadratic proraming and its simple correction, its line search is simple straight search and does not depend on any penalty function. Under suit assumptions, the algorithm is proved to possess global and superlinear convergence.展开更多
In this paper, the second order difference equation: △(rn△xn) + f(n, xn) = 0, n∈N(n0) (E) is considered. Some necessary and sufficient conditions for the oscillation of Eq.(E) are obtained.
Oscillatory behavior of solutions of second order nonlinear difference equation is studied. Oscillation criteria for its solutions are given. Examples are given in the text to illustrate the results.
First we establish the equivalence of the oscillation of the following two dif- ferential equations and (r(t)y'(t))' + τ^(-1)f(t, r(t -σ1(t))y(t),..., r(t -σn(t))y(t)) = 0. (**) Next, we establish the neces...First we establish the equivalence of the oscillation of the following two dif- ferential equations and (r(t)y'(t))' + τ^(-1)f(t, r(t -σ1(t))y(t),..., r(t -σn(t))y(t)) = 0. (**) Next, we establish the necessary and sufficient conditions of all solutions to (*) being oscillatory, when f is strongly superlinear or strongly sublinear.展开更多
基金supported by the National Natural Science Foundation of China(61374074)Natural Science Outstanding Youth Foundation of Shandong Province(JQ201119)Shandong Provincial Natural Science Foundation(ZR2012AM009,ZR2013AL003)
文摘We establish some new criteria for the oscillation of even order nonlinear dynamic equation. We study the case of strongly super-linear and the case of strongly sub-linear subject to various conditions.
文摘This paper presents a strong subfeasible directions algorithm possessing superlinear convergence for inequality constrained optimization. The starting point of this algorithm may be arbitary and its feasibility is monotonically increasing. The search directions only depend on solving one quadratic proraming and its simple correction, its line search is simple straight search and does not depend on any penalty function. Under suit assumptions, the algorithm is proved to possess global and superlinear convergence.
文摘In this paper, the second order difference equation: △(rn△xn) + f(n, xn) = 0, n∈N(n0) (E) is considered. Some necessary and sufficient conditions for the oscillation of Eq.(E) are obtained.
基金This research was supposed by the NSF of China (10071043)Shandong Province (Q2001A03).
文摘Oscillatory behavior of solutions of second order nonlinear difference equation is studied. Oscillation criteria for its solutions are given. Examples are given in the text to illustrate the results.
文摘First we establish the equivalence of the oscillation of the following two dif- ferential equations and (r(t)y'(t))' + τ^(-1)f(t, r(t -σ1(t))y(t),..., r(t -σn(t))y(t)) = 0. (**) Next, we establish the necessary and sufficient conditions of all solutions to (*) being oscillatory, when f is strongly superlinear or strongly sublinear.
