R. I. Parovik, “Generalized equations of Mathieu”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 2011, Number 2(3),Pages <nobr>12

This article is cited in 3 papers

MATHEMATICS

Generalized equations of Mathieu

R. I. Parovik^ab

^a Institute of Cosmophysical Researches and Radio Wave Propagation Far-Eastern Branch, Russian Academy of Sciences, 684034, Kamchatskiy Kray, Paratunka, Mirnaya st., 7, Russia
^b Branch of the Far Eastern Federal State University, 683 031, Petropavlovsk-Kamchatsky, Tushkanova st., 11 / 1, Russia

Abstract: We consider non-local model of wave process, which generalizes the classical model of parametric resonance Mathieu. It is proved that this model has a unique solution.

Keywords: Caputo-Gerasimov operator, Hille-Tamarkin formula, the integral Volterra of the second kind.

UDC: 517.955

MSC: 35C05

Received: 10.10.2011

DOI: 10.18454/2079-6641-2011-3-2-12-17