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STABILITY OF SOLUTIONS OF FIRST ORDER NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS WITH OSCILLATORY COEFFICIENTS 总被引:1,自引:0,他引:1
STABILITYOFSOLUTIONSOFFIRSTORDERNONLINEARNEUTRALDIFFERENTIALEQUATIONSWITHOSCILLATORYCOEFFICIENTS¥WangQiru(王其如)(LuoyangTeacher?.. 相似文献
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1IntroductionConsidertheneutraldifferentialequationswherepiERfori=l,2,...,m;o相似文献
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1 IntroductionConsider the second order quasilinear difference equationA(g(Ay.--l)) + f(n,y.) = 0, for n E N(no), (l'l)where A is defined by Ay. = Vn+1--yn, n E N(no) = {no, no + 1,'' }, nO E N = {l, 2,'. }.The following hold throughout the paPer:(H0) (i) g: R-R is a continuous increasing fUnction with propertiessgng(y) = sgny) g(R) = R;(il) f: N(no) x R--+ R is continuous as a function of y E R;(iii) yf(n,y) > 0 for n E N and y / 0.By a solution of the equation (1.l) we mean a non… 相似文献
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OSCILLATORY AND ASYMPTOTIC BEHAVIOR OF A CLASS OF FIRST ORDER NEUTRAL DIFFERENTIAL EQUATION WITH PIECEWISE CONSTANT DELAY 总被引:1,自引:0,他引:1
冯月才 《Annals of Differential Equations》2004,20(1):37-40
The oscillatory and asymptotic behavior of a class of first order nonlinear neutral differential equation with piecewise constant delay and with diverse deviating arguments are considered. We prove that all solutions of the equation are nonoscillatory and give sufficient criteria for asymptotic behavior of nonoscillatory solutions of equation. 相似文献
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1IntroductionTheexistence,uniqueness,oscillatoryandasymptoticbehaviorofsolutionsofthefirstorderdifferentialequationswithpiecewiseconstantdelayhavebeenstudiedin[1-4].Butoscillatoryandasymptoticbehavioroffirstorderneutraldifferentialequationwithpiecewiseconstantdelayseemtoberarelyconsidered[5,6].Inthispaper,weconsidertheoscillatoryandasymptoticbehavioroffirstordernonlinearneutraldifferentialequationwithpiecewiseconstantdeviatingargumentsoftheformwherecisaconstant,p(t)EC[0, co),fEC(R,R)andxf(x)… 相似文献
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P. Nesterov 《Journal of Difference Equations and Applications》2013,19(8):1173-1199
We propose an asymptotic summation method for certain class of linear difference systems. Both the ideas of the centre manifold theory and the averaging method are used to construct the asymptotics for solutions. We illustrate the asymptotic summation method by constructing the asymptotics for solutions of certain higher order scalar difference equation with an oscillatory decreasing coefficient. 相似文献
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M. Bartušek M. Cecchi M. Marini 《Journal of Mathematical Analysis and Applications》2006,320(1):108-120
Necessary and sufficient conditions for the existence of at least one oscillatory solution of a second-order quasilinear differential equation are presented. These results yield also new conditions guaranteeing the coexistence of oscillatory and nonoscillatory solutions. Our approach is based on the asymptotic representation of solutions by means of a periodic function and of a suitable zero-counting function. 相似文献
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The authors obtain results on the asymptotic behavior of the non-oscillatory solutions of a first order nonlinear neutral delay differential equation. A theorem giving sufficient conditions for all bounded solutions to be oscillatory is also proved. 相似文献
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In this paper, we deal with oscillatory and asymptotic properties of solutions of a fourth order sub-linear differential equation with the oscillatory operator. We establish conditions for the nonexistence of positive and bounded solutions and an oscillation criterion. 相似文献