This article is cited in 3 papers

A periodic boundary value problem for a fourth-order differential equation

A. R. Abdullaev^a, E. A. Skachkova<sup>b

a</sup> Chair of Higher Mathematics, Perm National Research Polytechnic University, 29 Komsomol'skii Ave., Perm, 614990 Russia
^b Chair of Mathematical Analysis, Perm State National Research University, 15 Bukirev str., Perm, 614990 Russia

Abstract: In this paper we obtain sufficient solvability conditions for a periodic boundary value problem for a fourth-order ordinary differential equation. The research technique is based on the solvability theorem for a quasilinear operator equation in the case of resonance. We formulate sufficient conditions for the existence of periodic solutions in terms of the original equation. We show that the main result of this paper clarifies the existence theorem established by B. Mehry and D. Shadman in Sci. Iran. 15 (2), 182–185 (2008).

Keywords: fourth-order differential equation, periodic solution, resonance.

UDC: 517.927

Received: 26.07.2012

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2013, 57:12, 1–7

Bibliographic databases:

•