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Currently displaying 1 – 4 of 4

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Neumann and periodic boundary-value problems for quasilinear ordinary differential equations with a nonlinearity in the derivative.

Girg, Petr — 2000

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of periodic solutions for a semilinear ordinary differential equation.

Girg, Petr — 1998

Electronic Journal of Differential Equations (EJDE) [electronic only]

Prüfer transformation for the $p$ -Laplacian.

Benedikt, Jiri; Girg, Petr — 2010

Electronic Journal of Differential Equations (EJDE) [electronic only]

Generalized trigonometric functions in complex domain

Petr Girg; Lukáš Kotrla — 2015

Mathematica Bohemica

We study extension of $p$ -trigonometric functions ${sin}_{p}$ and ${cos}_{p}$ to complex domain. For $p = 4, 6, 8, \dots$ , the function ${sin}_{p}$ satisfies the initial value problem which is equivalent to (*) $- {(u^{'})}^{p - 2} u^{''} - u^{p - 1} = 0, u (0) = 0, u^{'} (0) = 1$ in $ℝ$ . In our recent paper, Girg, Kotrla (2014), we showed that ${sin}_{p} (x)$ is a real analytic function for $p = 4, 6, 8, \dots$ on $(- π_{p} / 2, π_{p} / 2)$ , where $π_{p} / 2 = \int_{0}^{1} {(1 - s^{p})}^{- 1 / p}$ . This allows us to extend ${sin}_{p}$ to complex domain by its Maclaurin series convergent on the disc ${z \in ℂ : | z | < π_{p} / 2}$ . The question is whether this extensions ${sin}_{p} (z)$ satisfies (*) in the sense of differential equations in complex domain. This interesting...

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