Geodesic
A periodic boundary value problem for a~fourth-order differential equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2013), pp. 3-10

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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. 
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     author = {A. R. Abdullaev and E. A. Skachkova},
     title = {A periodic boundary value problem for a~fourth-order differential equation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--10},
     publisher = {mathdoc},
     number = {12},
     year = {2013},
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     url = {http://geodesic.mathdoc.fr/item/IVM_2013_12_a0/}
}
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A. R. Abdullaev; E. A. Skachkova. A periodic boundary value problem for a~fourth-order differential equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2013), pp. 3-10. http://geodesic.mathdoc.fr/item/IVM_2013_12_a0/