Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
linear integro-differential equation; periodic problem; distributed deviation; solvability
linear integro-differential equation; periodic problem; distributed deviation; solvability
Summary:
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.
References:
[1] Bravyi, E.: On solvability of periodic boundary value problems for second order linear functional differential equations. Electron. J. Qual. Theory Differ. Equ. 2016 (2016), Paper No. 5, 18 pages. DOI 10.14232/ejqtde.2016.1.5 | MR 3462810 | Zbl 1363.34211
[2] Bravyi, E. I.: On the best constants in the solvability conditions for the periodic boundary value problem for higher-order functional differential equations. Differ. Equ. 48 (2012), 779-786 Translation from Differ. Uravn. 48 2012 773-780. DOI 10.1134/S001226611206002X | MR 3180094 | Zbl 1259.34052
[3] Chiu, K.-S.: Periodic solutions for nonlinear integro-differential systems with piecewise constant argument. Sci. World J. 2014 (2014), Article ID 514854, 14 pages. DOI 10.1155/2014/514854
[4] Erbe, L. H., Guo, D.: Periodic boundary value problems for second order integrodifferential equations of mixed type. Appl. Anal. 46 (1992), 249-258. DOI 10.1080/00036819208840124 | MR 1167708 | Zbl 0799.45007
[5] Hardy, G. H., Littlewood, J. E., Pólya, G.: Inequalities. Cambridge Mathematical Library. Cambridge University Press, Cambridge (1988). MR 0944909 | Zbl 0634.26008
[6] Hu, S., Lakshmikantham, V.: Periodic boundary value problems for second order integro-differential equations of Volterra type. Appl. Anal. 21 (1986), 199-205. DOI 10.1080/00036818608839591 | MR 0840312 | Zbl 0569.45011
[7] Kiguradze, I. T.: Boundary-value problems for systems of ordinary differential equations. J. Sov. Math. 43 (1988), 2259-2339 Translated from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Novejshie Dostizh. 30 1987 3-103. DOI 10.1007/BF01100360 | MR 0925829 | Zbl 0782.34025
[8] Kiguradze, I., Půža, B.: On boundary value problems for functional-differential equations. Mem. Differ. Equ. Math. Phys. 12 (1997), 106-113. MR 1636865 | Zbl 0909.34054
[9] Mukhigulashvili, S., Partsvania, N., Půža, B.: On a periodic problem for higher-order differential equations with a deviating argument. Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74 (2011), 3232-3241. DOI 10.1016/j.na.2011.02.002 | MR 2793558 | Zbl 1225.34073
[10] Nieto, J.: Periodic boundary value problem for second order integro-ordinary differential equations with general kernel and Carathéodory nonlinearities. Int. J. Math. Math. Sci. 18 (1995), 757-764. DOI 10.1155/S0161171295000974 | MR 1347066 | Zbl 0837.45006
Search
Partner of
