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The zeros $c_{k} (ν)$ of the solution $z (t, ν)$ of the differential equation $z^{''} + q (t, ν) z = 0$ are investigated when $lim_{t \to \infty} q (t, ν) = 1$ , $\int^{\infty} | q (t, ν) - 1 | d t < \infty$ and $q (t, ν)$ has some monotonicity properties as $t \to \infty$ . The notion $c_{κ} (ν)$ is introduced also for $κ$ real, too. We are particularly interested in solutions $z (t, ν)$ which are “close" to the functions $sin t$ , $cos t$ when $t$ is large. We derive a formula for $d c_{κ} (ν) / d ν$ and apply the result to Bessel differential equation, where we introduce new pair of linearly independent solutions replacing the usual pair $J_{ν} (t)$ , $Y_{ν} (t)$ . We show the concavity of $c_{κ} (ν)$ for $| ν | \geq \frac{1}{2}$ and also...

Matematické texty a osobní počítače

Oldřich Ulrych; Jiří Veselý; Jaromír Vosmanský — 1990

Pokroky matematiky, fyziky a astronomie

Two-point boundary value problems for second order systems

Ravi P. Agarwal; Jaromír Vosmanský — 1983

Archivum Mathematicum

Necessary and sufficient conditions for the convergence of approximate Picard's iterates for nonlinear boundary value problems

Ravi P. Agarwal; Jaromír Vosmanský — 1985

Archivum Mathematicum

On two combinatorial identities

Leonard Carlitz; Josef Kaucký; Jaromír Vosmanský — 1982

Mathematica Slovaca

Preface

Ráb, Miloš; Vosmanský, Jaromír — 1973

Proceedings of Equadiff III

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The monotonicity of extremants of integrals of the differential equation $y^{''} + q (t) y = 0$

Monotonic properties of zeros and extremants of the differential equation $y^{''} + q (t) y = 0$

Certain higher monotonicity properties of $i$ -th derivatives of solutions of $y^{''} + a (t) y^{'} + b (t) y = 0$

Certain higher monotonicity properties of Bessel functions

Transformations of linear second order ordinary differential equations

[CDDE 2000. Proceedings of the colloquium on differential and difference equations, Brno, Czech Republic, September 5-8, 2000]. Preface

On solutions of differential equations with ``common zero'' at infinity

Matematické texty a osobní počítače

Two-point boundary value problems for second order systems

Necessary and sufficient conditions for the convergence of approximate Picard's iterates for nonlinear boundary value problems

On two combinatorial identities

Preface