The dirichlet boundary value problems for strongly singular higher-order nonlinear functional-differential equations
Open Access
- 26 March 2013
- journal article
- Published by Institute of Mathematics, Czech Academy of Sciences in Czechoslovak Mathematical Journal
- Vol. 63 (1) , 235-263
Abstract
Summary: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 conditionsKeywords
This publication has 7 references indexed in Scilit:
- Nonlocal boundary value problems for strongly singular higher-order linear functional-differential equationsElectronic Journal of Qualitative Theory of Differential Equations, 2013
- Two-point boundary value problems for strongly singular higher-order linear differential equations with deviating argumentsElectronic Journal of Qualitative Theory of Differential Equations, 2012
- On conditions for linear singular boundary value problems to be well posedDifferential Equations, 2010
- Singular Differential and Integral Equations with Applications2003
- Focal Boundary Value Problems for Differential and Difference Equations1998
- On two-point boundary value problems for systems of higher-order ordinary differential equations with singularitiesGeorgian Mathematical Journal, 1994
- On a singular multi-point boundary value problemAnnali di Matematica Pura ed Applicata (1923 -), 1970