Viewing Some Ordinary Differential Equations from the Angle of Derivative Polynomials

extensions of some polynomial inequalities to the polar derivative

توسیع تعدادی از نامساوی های چند جمله ای در مشتق قطبی

Some identities of degenerate Fubini polynomials arising from differential equations

Recently, Kim et al. have studied degenerate Fubini polynomials in [T. Kim, D. V. Dolgy, D. S. Kim, J. J. Seo, J. Nonlinear Sci. Appl., 9 (2016), 2857–2864]. Jang and Kim presented some identities of Fubini polynomials arising from differential equations in [G.-W. Jang, T. Kim, Adv. Studies Contem. Math., 28 (2018), to appear]. In this paper, we drive differential equations from the generating ...

On the Oscillatory Integration of Some Ordinary Differential Equations

Conditions are given for a class of nonlinear ordinary differential equations x′′ + a(t)w(x) = 0, t ≥ t0 ≥ 1, which includes the linear equation to possess solutions x(t) with prescribed oblique asymptote that have an oscillatory pseudo-wronskian x′(t)− x(t) t .

Solutions Approaching Polynomials at Infinity to Nonlinear Ordinary Differential Equations

This paper concerns the solutions approaching polynomials at ∞ to n-th order (n > 1) nonlinear ordinary differential equations, in which the nonlinear term depends on time t and on x, x′, . . . , x(N), where x is the unknown function and N is an integer with 0 ≤ N ≤ n − 1. For each given integer m with max{1, N} ≤ m ≤ n− 1, conditions are given which guarantee that, for any real polynomial of d...

Fractional differential equations with Legendre polynomials