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Existance of boundary problem solution for quasilinear functional and differential equation


The article is devoted an actual problem of solvability of nonlinear boundary value problems for the differential equations. On the basis of the differential inequality, which are analogue of a known differential inequality of Tchaplygin, for the ordinary differential equation of the first order, the theorem of existence and limitation of the solution of a boundary value problem for the quasilinear functional differential equation with aftereffect is proved. During the proof the original boundary value problem is reduced to some operational equation with completely continuous operator. Work is executed with support of the Russian Fundamental Researches Fund and administration of Perm region (project № 10-01-96054-р_ural-а) and ZAO "PROGNOZ".


functional differential equation of the second order; sign on Green's function

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