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In this paper, sufficient conditions have been obtained for oscillation/nonoscillation of a class of homogeneous/nonhomogeneous linear difference equations of third order. 相似文献
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In this paper, we consider a food-limited population model with impulsive effect. Several explicit sufficient conditions are established for oscillation and nonoscillation of solutions of the equations. 相似文献
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Alexander Domoshnitsky 《Journal of Mathematical Analysis and Applications》2007,329(1):238-267
The paper is devoted to the maximum principles for functional equations in the space of measurable essentially bounded functions. The necessary and sufficient conditions for validity of corresponding maximum principles are obtained in a form of theorems about functional inequalities similar to the classical theorems about differential inequalities of the Vallee Poussin type. Assertions about the strong maximum principle are proposed. All results are also true for difference equations, which can be considered as a particular case of functional equations. The problems of validity of the maximum principles are reduced to nonoscillation properties and disconjugacy of functional equations. Note that zeros and nonoscillation of a solution in a space of discontinuous functions are defined in this paper. It is demonstrated that nonoscillation properties of functional equations are connected with the spectral radius of a corresponding operator acting in the space of essentially bounded functions. Simple sufficient conditions of nonoscillation, disconjugacy and validity of the maximum principles are proposed. The known nonoscillation results for equation in space of functions of one variable follow as a particular cases of these assertions. It should be noted that corresponding coefficient tests obtained on this basis cannot be improved. Various applications to nonoscillation, disconjugacy and the maximum principles for partial differential equations are proposed. 相似文献
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In this paper, the structure of the solution space of y n +3 + ry n +2 + qy n +1 + py n =0, n S 0, is studied, keeping oscillatory/nonoscillatory behaviour of solutions of the equation in view, where p , q and r are constants. Some of these results are generalized partially to hold for y n +3 + r n y n +2 + q n y n +1 + p n y n =0, n S 0, where { p n }, { q n } and { r n } are sequences of real numbers. 相似文献
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Baoguo Jia 《Journal of Mathematical Analysis and Applications》2009,349(2):556-567
We obtain Wong-type comparison theorems for second order linear dynamic equations on a time scale. The results obtained extend and are motivated by Wong's comparison theorems. As a particular application of our results, we show that the difference equation
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一类拟线性二阶微分方程解的振动与非振动的判定 总被引:4,自引:0,他引:4
本文讨论了拟线性微分方程(p(x'))'+q(t)p(x)=0,t≥t0,q(t)≥0(这里 p(u)=|u|p-1u,p>0是常数)的解的振动与非振动条件,并改进了文献[2]的结果. 相似文献
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Some nonoscillation criteria for quasilinear second order differential equations are obtained. These results generalize the classical results of Hille, Wintner and Opial and recent results of Elbert, Yan, Del Pino as well as Takasi and Yoshida. 相似文献