On nonlocal problems for ordinary differential equations and on a nonlocal parabolic transmission problem. (1999)

• Record Type: Journal Article
• Authors: Denche, M.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 12:Number 3(1999)
• Page Start: 279
• Page End: 291
• Publication Date: 1999
• Subjects: nonlocal problems -- ordinary differential equations -- parabolic differential equation -- boundary and transmission conditions -- coerciveness estimate -- completeness -- root functions -- elementary solutions; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S104895339900026X
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : In the present paper we study nonlocal problems for ordinary differential equations with a discontinuous coefficient for the high order derivative. We establish sufficient conditions, known as regularity conditions, which guarantee the coerciveness for both the space variable and the spectral parameter, as well as guarantee the completeness of the system of root functions. The results obtained are then applied to the study of a nonlocal parabolic transmission problem.