Geodesic
The periodic problem for the second order integro-differential equations with distributed deviation
Mathematica Bohemica, Tome 146 (2021) no. 2, pp. 167-183.

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We study the question of the unique solvability of the periodic type problem for the second order linear integro-differential equation with distributed argument deviation $$ u''(t)=p_0(t)u(t)+\int _{0}^{\omega }p(t,s)u(\tau (t,s)) {\rm d}s+ q(t), $$ and on the basis of the obtained results by the a priori boundedness principle we prove the new results on the solvability of periodic type problem for the second order nonlinear functional differential equations, which are close to the linear integro-differential equations. The proved results are optimal in some sense.
DOI : 10.21136/MB.2020.0061-19
Classification : 34B15, 34K06, 34K13
Keywords: linear integro-differential equation; periodic problem; distributed deviation; solvability 
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Mukhigulashvili, Sulkhan; Novotná, Veronika. The periodic problem for the second order integro-differential equations with distributed deviation. Mathematica Bohemica, Tome 146 (2021) no. 2, pp. 167-183. doi : 10.21136/MB.2020.0061-19. http://geodesic.mathdoc.fr/articles/10.21136/MB.2020.0061-19/

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