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SOLVABILITY OF NONLINEAR BOUNDARY VALUE PROBLEMS FOR A NONLINEAR FUNCTIONAL-DIFFERENTIAL EQUATION OF THE SECOND ORDER

Annotation

A nonlinear functional-differential equation of the second order of neutral type is considered in this article. The sufficient conditions of existence of solution of some boundary value problems for this equation are presented.

Keywords

functional-differential equation; nonlinear boundary value problem; Green function

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UDC

517.929

Pages

1255-1260

References

1. Azbelev N.V., Rahmatullina L.F. K voprosu o funkcional'no-differencial'nyh neravenstvah i monotonnyh operatorah // Funkc.-differenc. uravnenija. Perm': Izd-vo Perm. politeh. in-ta, 1986. C. 3–9. 2. Azbelev N.V., Maksimov V.P., Rahmatullina L.F. Vvedenie v teoriju funkcional'no-differencial'nyh uravnenij. M.: Nauka, 1991. 3. Azbelev N.V., Maksimov V.P., Rahmatullina L.F. Jelementy sovremennoj teorii funkcional'no-differencial'nyh uravnenij. Metody i prilozhenija. M.: Institut komp'juternyh issledovanij, 2002. 4. Kantorovich L.V., Vulih B.Z., Pinsker A.G. Funkcional'nyj analiz v poluuporjadochennyh prostranstvah. Moskva; Leningrad: Gostehizdat, 1950. 5. Hatson V., Pim Dzh. Prilozhenija funkcional'nogo analiza i teorii operatorov. M.: Mir, 1983. 6. Larionov A.S., Cimonov P.M., Sheina M.V. Uslovija razreshimosti nachal'noj zadachi dlja sistem nelinejnyh funkcional'no-differencial'nyh uravnenij // Vestnik Tambovskogo universiteta. Serija Estestvennye i tehnicheskie nauki. Tambov, 2010. T. 15. Vyp. 2. S. 542-549. 7. Domoshnickij A.I. O spravedlivosti teoremy Chaplygina dlja uravnenij nejtral'nogo tipa // Kraevye zadachi. Perm. politehn. in-t. Perm'. 1981. S. 121-125. 8. Larionov A.S. Priznaki sohranenija znaka funkcii Grina nekotoryh kraevyh zadach dlja differencial'nogo uravnenija vtorogo porjadka s zapazdyvajushhim argumentom // Vestnik grazhdanskih inzhenerov. 2008. № 1(14). S. 85-89.

Received

2015-06-17

Section of issue

Scientific articles

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