EUDML

Suppose that the function $q (t)$ in the differential equation (1) $y^{''} + q (t) y = 0$ is decreasing on $(b, \infty)$ where $b \geq 0$ . We give conditions on $q$ which ensure that (1) has a pair of solutions $y_{1} (t), y_{2} (t)$ such that the $n$ -th derivative ( $n \geq 1$ ) of the function $p (t) = y_{1}^{2} (t) + y_{2}^{2} (t)$ has the sign ${(- 1)}^{n + 1}$ for sufficiently large $t$ and that the higher differences of a sequence related to the zeros of solutions of (1) are ultimately regular in sign.

Page 1

Download Results (CSV)

Advanced Search

Formula preview

Currently displaying 1 – 9 of 9

Some Characterizations of the Gamma Function Involving the Notion of Complete Monotonicity.

Some monotonicity properties and characterizations of the gamma function.

Some Characterizations of the Gamma Function involving the Notion of Complete Monotonicity (Short Communication)

Some monotonicity properties and characterizations of the gamma function. (Short Communication).

On the zeros of a function related to Bessel functions

Further higher monotonicity properties of Sturm-Liouville functions

On the zeros of some special functions: differential equations and Nicholson-type formulas

Inequalities for the smallest zeros of Laguerre polynomials and their $q$ -analogues.

Transcendentality of zeros of higher derivatives of functions involving Bessel functions.