Abstract
The general linear boundary value problem for an abstract functional differential equation is considered in the case that the number of boundary conditions is greater than the dimension of the null-space to the corresponding homogeneous equation. Sufficient conditions of the solvability of the problem are obtained. A case of a functional differential system with aftereffect is considered separately.
Highlights
1 Introduction Linear boundary value problems (BVPs) for differential equations with ordinary derivatives that lack the everywhere and unique solvability are met with in various applications. Among these applications are some problems in oscillation theory and economic dynamics [ ]
We consider a case that the number of linearly independent boundary conditions is greater than the dimension of the null-space of the corresponding homogeneous equation and obtain sufficient conditions of the solvability without recourse to the adjoint BVP and an extension of the original BVP
Our approach is based in essence on the assumption that the derivative of the solution does belong to a Hilbert space
Summary
1 Introduction Linear boundary value problems (BVPs) for differential equations with ordinary derivatives that lack the everywhere and unique solvability are met with in various applications. General results concerning linear BVPs for an abstract functional differential equation (AFDE) are given in [ ]. M] : D → Rm be a linear bounded vector functional with linearly independent components, γ = col(γ , .
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