[PDF] Top 20 Wiman’s formula for a second order dynamic equation

... A solution u(·) of (.) is said to have a zero at a ∈ T if u(a) = , and it has a node at a+σ  (a) if u(σ (a))u(a) < . A generalized zero of u(t) is defined as its zero or its node. A solution of (.) is said to be ... See full document

... of Equation (1) is said to be oscillatory on [ t 0 , ∞ )  in case it is neither eventually positive nor eventually negative; otherwise, the solution is said to be ...nonoscillatory. Equation (1) is said to ... See full document

... This paper emphasizes on a new direct numerical solver of second order ordinary differential equations (ODEs). We developed this solver using block backward differentiation formula (BBDF) method with ... See full document

... an equation admits a second order formal recursion operator but does not satisfy the first order integrability conditions, then the square root of the recursion operator cannot be computed in ... See full document

... concerning dynamic equations with impulses on time scales (see [4, 5, 16] for earlier ...discontinuous dynamic equations on a time scale subject to fixed-time impulses and nonlinear boundary ... See full document

... Ji et al Advances in Difference Equations 2013, 2013 340 http //www advancesindifferenceequations com/content/2013/1/340 R ES EARCH Open Access On oscillation of second order neutral dynamic equations[.] ... See full document

... that Equation (6) satisfies a nonlinear differential equation of the second order in time, tacking into account the (experimentally established) slow variation in time of the coefficient ... See full document

... The purpose of writing this article is to show some spectral properties of the Bessel operator equation, with spectral parameter-dependent boundary condition. This problem arises upon separation of variables in ... See full document

... S.enel, Oscillation theorems for the second order damped nonlinear dynamic equation on time scales, Contemp. Zhang, Oscillation of second-order half-linear delay dynamic equations with d[r] ... See full document

... differential equation of second order and finds the numerical solutions of second order differential equations with the various ...the second order differential ... See full document

... where f : [,T ] × [, ∞ ) × R → R and h : [, T ] → (, ∞ ) are continuous functions. Our study is motivated by current activity of many researchers in the area of theory and appli- cations of PVBPs; see, for example, ... See full document

... fourth-order equation where the linear part is given by the second derivative of an invertible second-order ...The equation includes a deviating argument and the boundary ... See full document

... The first author was supported by Grants 201/07/0145 and 201/10/1032 of the Czech Grant Agency Prague and by the Council of Czech Government MSM 0021630529. The second author was supported by Grants 201/07/0145 ... See full document

... Theorem  Under the assumptions (.) and (.), all the solutions of (.) are bounded. The main idea of our proof is acquired from []. The proof of Theorem  is based on a small twist theorem due to Ortega []. It ... See full document

... the second-order delay equation () as well as Equation () (for Equation (), see ...of Equation (). Since the nonlinearity of Equation () explicitly contains the ... See full document

... In this paper, we study in particular developable surfaces, a special type of ruled surface in the Lorentzian Heisenberg group Heis 3.. We find out explicit paramet-.[r] ... See full document

... [7] P. M. Dhakane, On global existence of solutions of an abstract nonlinear functional second order inte- grodifferential equation, Proceeding of International Conference on Mathematical Science in ... See full document

... In recent years, the study of the existence of analytic solutions of iterative functional differential equations has attracted several researchers, see [2–11] and references cited therein. In [3], the authors studied the ... See full document

... Equation (1.3) was studied in detail in [7, 10], where we have found the region of param- eters for which the equilibrium is globally asymptotically stable and the region where the equation has a unique ... See full document

... It is important to note that many nonlinear difference equations and systems can be reduced to some special cases of equation (), which means that they are solvable too. Some interest in the area has been renewed ... See full document