[PDF] Top 20 Existence and uniqueness of solutions to the second order fuzzy dynamic equations on time scales

... Recently, one of the most interesting and significant discussions in the field of differential equations is dynamic equations on time scales. The valuable applications of these equa- tions ... See full document

... the existence and uniqueness of solutions of fuzzy nabla dynamic equations on time scales under Hukuhara ...establish existence and uniqueness ... See full document

... Since f is continuous, T is continuous and it can be shown that T is a compact oper- ator by the Arzela-Ascoli theorem. Therefore, Theorem 1.8 is applicable to T and T must have a fixed point. Hence the BVP has a ... See full document

... prove existence and uniqueness results in the presence of coupled lower and upper solutions for the general nth problem in time scales with linear dependence on the ith ∆ - derivatives ... See full document

... the solutions of impulsive dynamic equations on time scales, such as the method of lower and upper solutions, fixed-point theory ...on time scales, which were first ... See full document

... of (1.1) is called oscillatory if it is neither eventually positive nor eventually negative; otherwise it is called nonoscillatory. Equation (1.1) is called oscillatory if all solutions are oscillatory. Our ... 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 ... See full document

... functional dynamic equation on time scales and obtained sufficient conditions for the existence of positive ...the existence of at least twin positive solutions to the following ... See full document

... of time scales in his ...of time scale calculus can be found in [–] and omitted ...the existence of nonoscilla- tory solutions to neutral dynamic equations on ... See full document

... on time scales is now an active area of ...on time scales unifies the study of both discrete and continuous processes, besides many ...of time scales was initiated by Stefan ... See full document

... volve the behavior of the integral of the coe ffi cients r and p. On the other hand, the oscillatory properties can be described by the so-called Reid roundabout theorem (cf. [5, 11, 23]). This theorem shows the connection ... See full document

... the second-order and three-order p-Laplacian differential equation, see 1–8 and the references ...the existence of periodic solutions for a p-Laplacian Li´enard differential equation with ... See full document

... of solutions of various equations on time scales, and we refer the reader to Bohner and Saker 5 , Erbe 6 , and Hassan 7 ...the solutions of delay dynamic equations on ... See full document

... functional dynamic equation on a time scale and obtained sufficient conditions for the existence of positive ...positive solutions of boundary value problem BVP for short ... See full document

... Saker, “Oscillation of second-order forced nonlinear dynamic equations on time scales,” Electronic Journal of Qualitative Theory of Differential Equations, no.. Ridenhour, “Hamiltonian sy[r] ... See full document

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

... of time scales, which unifies continuous and discrete analysis, was first introduced by Hilger ...for dynamic equations on time scales has recently received a lot of attention, ... See full document

... of dynamic equations on time scales goes back to its founder Stefan Hilger 8 and is a new area of still fairly theoretical exploration in ...that dynamic equations on time ... See full document

... a dynamic analog of the BVPs ...the existence of at least one positive solution were studied for the BVPs ...the existence of at least one or three positive solutions for the BVP ... See full document

... Neutral equations find numerous applications in natural science and ...the existence of equations of ...the existence of nonoscillatory solutions for neutral delay dynamic ... See full document