Abstract
The a priori boundedness principle is proved for the two-point right-focal boundary value problems for strongly singular higher-order nonlinear functional-differential equations. Several sufficient conditions of solvability of the two-point right-focal problem under consideration are derived from the a priori boundedness principle. The proof of the a priori boundedness principle is based on 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 right-focal boundary conditions.
Highlights
The a priori boundedness principle is proved for the two-point right-focal boundary value problems for strongly singular higher-order nonlinear functional-differential equations
The principles of the theory of singular boundary value problems were built by Kiguradze in his study [ ]
The first step in studying the differential equations with strong singularities was made by Agarwal and Kiguradze in the article [ ], where the linear ordinary differential equations under conditions ( . ), in the case when the functions pj have strong singularities at the points a and b, are studied
Summary
The a priori boundedness principle is proved for the two-point right-focal boundary value problems for strongly singular higher-order nonlinear functional-differential equations. 1.2 Theorems on the solvability of problem (1.1), (1.2) Define the operator P : C m– (]a, b]) × C m– (]a, b]) → Lloc(]a, b]) by the equality m Let the operator P be γ consistent with boundary condition
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