The periodic problem for the second order integro-differential equations with distributed deviation
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In the paper we describe the classes of unique solvability of the Dirichlet and mixed two point boundary value problems for the second order linear integro-differential equation b u (t) = p0 (t)u(t) + p1 (t)u(1 (t)) + p(t, s)u( (s)) ds + q(t). a On the basis of the obtained and, in some sense, optimal results for the linear problems, by the a priori boundedness principle we prove the theorems of solvability and unique solvability for the second order nonlinear functional differential equations under the mentioned boundary conditions.
KeywordsIntegro-differential equations, Dirichlet and mixed problems, unique solvability, a priori boundedness principle
Document typePeer reviewed
Document versionFinal PDF
SourceMathematica Bohemica. 2021, vol. 146, issue 2, p. 167-183.
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