[PDF] Top 20 Behavior of solutions of a third order dynamic equation on time scales

... oscillatory behavior, we suppose that the time scale under con- sideration is not bounded above, ...a time scale interval of the form [a, ...satisfying equation () for t ≥ ...nonoscillatory. ... See full document

... the third-order neutral dynamic equations on time scales in the case p(t) ≥ ...asymptotic behavior of solutions of ... See full document

... T : a ≤ t ≤ b } . The jump operators σ and ρ allow the classification of points in a time scale in the following way. If σ(t) > t, the point t is right-scattered, while if ρ(t) < t then t is left-scattered. ... See full document

... of time scales, which has recently received a lot of attention, was introduced by Hilger’s landmark paper 1 in order to create a theory that can unify continuous and discrete ...a time scale ... See full document

... certain third-order delay and advanced dynamic equations on unbounded time ...A time scale T is a nonempty closed subset of the real ... See full document

... oscillatory behavior of dynamic equation with mixed arguments on time ...of third order dynamic equation with mixed ar- guments of type ...all solutions of ... See full document

... Remark 3.4 It is not easy to find a sufficient condition for the existence of nonoscillatory solutions tending to zero to (1) since their asymptotic behaviors are more complex than those of other solutions. ... See full document

... on time scales, the new periodicity concept for time scales and some important theorems which will be needed to show the existence and nonexistence of pe- riodic solutions in shifts δ ± ... See full document

... A time scale is a nonempty arbitrary closed subset of ...of time scale in 1988 in order to unify the theory of continuous and discrete ...The time scales approach not only unifies ... See full document

... of solutions of various equations on time-scales; we refer the reader to the papers 6–38 ...of third-order dynamic equations; see, for example, 14– 16, 21, 35 ...the ... See full document

... Saker, Asymptotic Behavior of Solutions of a Third-Order Non-linear Dynamic Equation on Time Scales, Journal of Computational and Applied Mathematics 181, (2005) 92-102. Thandapani, O[r] ... See full document

... the Equation (4). In [18], Gao et al. considered the third-order nonlinear dynamic Equation ...of Equation (1) is oscillatory or converges to ...of Equation (1) is ... See full document

... of solutions to second order fuzzy dynamic equations on time ...of solutions to second order fuzzy dynamic equations on time ... See full document

... of third-order nonlinear dynamic equations with nonpositive neutral coefficients on time scales by a generalized Riccati transformation and employing functions in some function ... See full document

... of dynamic equations on time scales has been a new important mathematical branch [–] since it was initiated by Hilger ...same time, the boundary value problems of impulsive dynamic ... See full document

... Neutral equations find numerous applications in natural science and technology. For instance, they are frequently used for the study of distributed networks containing lossless transmission lines. So, we try to establish ... See full document

... Verify that with v = 0 and M = 1, (v , M) is a solution-tube of (3.14). By Theorem 3.12, the problem (3.14) has a solution x such that |x(t)| ≤ 1 for every t ∈ (0, 1] T . Observe that α = v− M and β = v+ M are, ... See full document

... We will establish some new criteria of oscillatory and asymptotic behavior for Eq. (1.1) based on the properties of conformable fractional differential and integral together with a generalized Riccati ... See full document

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

... A time scale T is an arbitrary nonempty closed subset of the real ...of time scales. On a time scale T , the forward jump operator, the backward jump operator and the graininess function are ... See full document