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.

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Higher monotonicity properties of zero points of the linear combination of the solution and its first derivative of the differential equation $y^{''} + q (t) y = 0$

Contribution to the monotonicity of the sequence of zero points of integrals of the differential equation $y^{''} + g (t) y = 0$ with regard to the basis $[α, β]$

A note on higher monotonicity properties of certain Sturm Liouville functions

A remark to one result of M. E. Muldoon

On a certain modification of Sturm's comparison theorem

Generalization of amplitude phase and accompanying differential equation

Some analogues for higher monotonicity of the Sonin-Butlewski-Pólya theorem

A note on higher monotonicity properties of certain Sturm-Liouville functions. III

A note on higher monotonicity properties of certain Sturm-Liouville functions. II.

A note on higher monotonicity properties of generalized Airy functions

Lineárne homogénne diferenciálne rovnice druhého rádu rýdzo diskonjugované vzhľadom na derivácie

Further higher monotonicity properties of Sturm-Liouville functions