Czechoslovak Mathematical Journal, Vol. 63, No. 1, pp. 235-263, 2013

The Dirichlet boundary value problems for strongly singular higher-order nonlinear functional-differential equations

Sulkhan Mukhigulashvili

Sulkhan Mukhigulashvili, Mathematical Institute, Academy of Sciences of the Czech Republic, Žižkova 22, 616 62 Brno, Czech Republic; I. Chavchavadze State University, Faculty of physics and mathematics, I. Chavchavadze St. No. 32, Tbilisi 0179, Georgia, e-mail: mukhig@ipm.cz

Abstract: 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.

Keywords: higher order functional-differential equation, Dirichlet boundary value problem, strong singularity, Fredholm property, a priori boundedness principle

Classification (MSC 2010): 34K06, 34K10


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