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Keywords:
higher order functional-differential equation; Dirichlet boundary value problem; strong singularity; Fredholm property; a priori boundedness principle
higher order functional-differential equation; Dirichlet boundary value problem; strong singularity; Fredholm property; a priori boundedness principle
Summary:
The a priori boundedness principle is proved for the Dirichlet boundary value problems for strongly singular higher-order nonlinear functional-differential equations. Several sufficient conditions of solvability of the Dirichlet problem under consideration are derived from the a priori boundedness principle. The proof of the a priori boundedness principle is based on the Agarwal-Kiguradze type theorems, which guarantee the existence of the Fredholm property for strongly singular higher-order linear differential equations with argument deviations under the two-point conjugate and right-focal boundary conditions.
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