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

Sulkhan Mukhigulashvili

Czechoslovak Mathematical Journal (2013)

  • Volume: 63, Issue: 1, page 235-263
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Mukhigulashvili, Sulkhan. "The Dirichlet boundary value problems for strongly singular higher-order nonlinear functional-differential equations." Czechoslovak Mathematical Journal 63.1 (2013): 235-263. <http://eudml.org/doc/252464>.

@article{Mukhigulashvili2013,
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.},
author = {Mukhigulashvili, Sulkhan},
journal = {Czechoslovak Mathematical Journal},
keywords = {higher order functional-differential equation; Dirichlet boundary value problem; strong singularity; Fredholm property; a priori boundedness principle; higher order functional-differential equation; two-point boundary value problem; strong singularity; solvability},
language = {eng},
number = {1},
pages = {235-263},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The Dirichlet boundary value problems for strongly singular higher-order nonlinear functional-differential equations},
url = {http://eudml.org/doc/252464},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Mukhigulashvili, Sulkhan
TI - The Dirichlet boundary value problems for strongly singular higher-order nonlinear functional-differential equations
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 1
SP - 235
EP - 263
AB - 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.
LA - eng
KW - higher order functional-differential equation; Dirichlet boundary value problem; strong singularity; Fredholm property; a priori boundedness principle; higher order functional-differential equation; two-point boundary value problem; strong singularity; solvability
UR - http://eudml.org/doc/252464
ER -

References

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