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A generalized solution of the differential equation 1 in the class is any generalized function in satisfying equation 1 in , that is, for any test function , the equation must be satisfied. Here is the operator adjoint to in the sense of Lagrange: A generalized solution of a boundary value problem should satisfy the boundary condition in the appropriate generalized sense in or , etc.
References  S. Sobolev, "Applications of functional analysis in mathematical physics" , Amer.
Gel'fand, G. Komatsu ed.
Generalized solutions of variational problems and applications : Advances in Nonlinear Analysis
Katata, , Lect. Vladimirov, "Equations of mathematical physics" , M. Dekker Translated from Russian  V. Euler, "Institutionum calculi integralis" G. Kowalewski ed.
How to Cite This Entry: Generalized solution. Boundary-value problems for elliptic functional-differential equations and their applications.
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Funding : Russian Foundation for Basic Research. Ministry of Education and Science of the Russian Federation.
Generalized solutions of mixed problems for first-order partial functional differential equations.
This research was supported by the Russian Foundation for Basic Research grant no. PDF file kB.
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