[PDF] Top 20 Positive Solutions to Singular and Delay Higher-Order Differential Equations on Time Scales

... The authors would like to thank the referees for helpful comments and suggestions. The work was supported partly by the NSF of China 10771202, the Research Fund for Shanghai Key Laboratory of Modern Applied Mathematics ... See full document

... Impulsive delay differential equations may express several real-world simulation processes which depend on their prehistory and are subject to short-time ... See full document

... eventually positive nor eventually negative, otherwise it is called ...of time scales, which has recently received a lot of attention, was introduced by Stefan Hilger in [] in order to unify ... See full document

... Motivated by the above mentioned work, in this paper, we present some limit type con- ditions and discuss the existence and multiplicity of positive solutions of the singular frac- tional multi-point ... See full document

... a time scale, for any a, b ∈ R −∞, ∞b > a, the interval a, b defined as a, b {t ∈ T | a ≤ t ≤ ...dynamic equations on time scales, the reader may refer to 1–3 for an introduction to the ... See full document

... the positive solutions of a higher-order singular fractional differential system with coupled integral boundary ...one positive solution are established together with the ... See full document

... differential equations, which provide a natural description of memory and hereditary properties of various materials and processes, are regarded as an important mathematical tool for better understanding of many ... See full document

... For n = 2, v = 0, in the case of ordinary differential equations, BVPs analogous to (1.1) with singularity has been widely studies by many authors, see,for example, [12,15-17]. For the case τ = 0, v = 0, ... See full document

... differential equations arise from the studies of complex problems in many disciplinary areas such as fluid flows, electrical net- works, rheology, biology chemical physics, and so ...of positive ... See full document

... periodic solutions for delayed differential equations is an important research topic in ODE qualitative analysis, which has wide applications in mechanics, physics, ecology, economics, and other disciplines ... See full document

... In order to create a theory that can unify discrete and continuous analysis, the theory of time scale was initiated by Hilger’s landmark paper [], which has received a lot of at- ...interesting time ... See full document

... strictly positive absolutely continuous function. Such equations, even in the case p ≡ , where they are referred to as being of Schrödinger or Klein-Gordon type, ap- pear in many scientific areas including ... See full document

... Step 1. If u has no zero in 0, ∞, then ut < 0 for t ≥ 0 and, by Lemma 2.5, u fulfils 2.21. Step 2. Assume that θ > 0 is the first zero of u on 0, ∞. Then, due to Remark 2.4, u θ > 0. Let ut > 0 for t ∈ θ, ∞. ... See full document

... of time scales, which has recently received a lot of attention, was introduced by Hilger in his ...in order to unify continuous and discrete analysis see Hilger ...of time scales, by ... See full document

... where f : T × R → R , τ : T → T is a delay function and T is a time scale. We formulate the principle which gives the guarantee that the graph of at least one solution of the above mentioned equation stays ... See full document

... and higher-order differential equations have been widely studied by many authors, who have provided many techniques for obtaining oscillatory criteria for fourth- and higher-order ... See full document

... two positive solutions to a class of nonlinear first-order periodic boundary value problems of impulsive dynamic equations on time scales are ... See full document

... where a min{0, inf{τ t : 0 ≤ t ≤ 1}}, b max{1, sup{τt : 0 ≤ t ≤ 1}}, and the existence of positive solutions to 1.1 is obtained. When τt t − r in 1.1, Agarwal and O’Regan in 5, Lin and Xu in 6 discussed the ... See full document

... of solutions (or positive so- lutions) of nonlinear initial fractional differential equations by the use of techniques of nonlinear analysis (fixed point theorems, Leray-Schauder theory, ... See full document

... To seek necessary and sufficient conditions for the existence of solutions to the ordinary differential equations is important and interesting, but difficult. Professors Wei 16, 17, Du and Zhao 18, Graef and ... See full document