On Two-point Boundary Value Problems for Second Order Singular Functional Differential Equations

KIGURADZE, Ivan and Bedřich PŮŽA. On Two-point Boundary Value Problems for Second Order Singular Functional Differential Equations. Functional Differential Equations. Israel: The College of Judea and Samaria, 2005, 12/2005, 3-4, p. 271-294. ISSN 0793-1786.

Basic information

• Original name: On Two-point Boundary Value Problems for Second Order Singular Functional Differential Equations
• Name in Czech: O 2-bodových okrajových úlohách pro singulární diferenciální rovnici druhého řádu
• Authors: KIGURADZE, Ivan (268 Georgia) and Bedřich PŮŽA (203 Czech Republic, guarantor).
• Edition: Functional Differential Equations, Israel, The College of Judea and Samaria, 2005, 0793-1786.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: Israel
• Confidentiality degree: is not subject to a state or trade secret
• RIV identification code: RIV/00216224:14310/05:00013879
• Organization unit: Faculty of Science
• Keywords in English: second order singular functional differential equations; two-point boundary value problems; unique solvability; stability
• Tags: stability, two-point boundary value problems, unique solvability

Abstract

For the functional differential equations u(t)= f(u)(t) with the continuous operator f from C1loc(]a,b[)to L1loc(]a,b[)the unimprovable, in a certain sense, sufficient conditions for the solvability and unique solvability of the two-point boundary value problems u(a+)=0=u(b-) and u(a+)=0=u(b-) are established. These condition cover the case when for an arbitrary u the function f(u) is not integrable on [a,b], having singularities at the points a and b.

Abstract (in Czech)

Pro funkcionální diferenciální rovnici u(t)= f(u)(t) se spojitým operátorem f z C1loc(]a,b[)do L1loc(]a,b[) jsou odvozeny v jistém smyslu nezlepšitelné postačující podmínky existence a jednoznačné existence řešení 2-bodových okrajových úloh u(a+)=0=u(b-) a u(a+)=0=u(b-). Podmínky obsahují i případy, kdy pro nějaká u není funkce f(u) integrabilní na [a,b], přesněji, kdy má singularity v bodech a a b.

Links

• MSM 143100001, plan (intention): Name: Funkcionální diferenciální rovnice a matematicko-statistické modely

Investor: Ministry of Education, Youth and Sports of the CR, Functional-differential equations and mathematical-statistical models

• MSM0021622409, plan (intention): Name: Matematické struktury a jejich fyzikální aplikace

Investor: Ministry of Education, Youth and Sports of the CR, Mathematical structures and their physical applications