Geodesic
The Dirichlet boundary value problems for strongly singular higher-order nonlinear functional-differential equations
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 1, pp. 235-263.

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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.
DOI : 10.1007/s10587-013-0016-2
Classification : 34K06, 34K10, 34K12
Keywords: higher order functional-differential equation; Dirichlet boundary value problem; strong singularity; Fredholm property; a priori boundedness principle 
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Mukhigulashvili, Sulkhan. The Dirichlet boundary value problems for strongly singular higher-order nonlinear functional-differential equations. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 1, pp. 235-263. doi : 10.1007/s10587-013-0016-2. http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0016-2/

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