THE NONLOCAL BOUNDARY VALUE PROBLEMS FOR STRONGLY SINGULAR HIGHER-ORDER NONLINEAR FUNCTIONAL-DIFFERENTIAL EQUATIONS - Mukhigulashvili, Sulkhan (Italian Journal of Pure and Applied Mathematics, 2015)
A priori boundedness principle is proven for the nonlocal boundary value problems for strongly singular higher-order nonlinear functional-differential equations. Several suffcient 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 nonlocal boundary conditions.