Nonlocal boundary value problem in terms of flow for Sturm-Liouville operator in differential and difference statements

Author:

Dovletov Dovlet M.1

Affiliation:

1. Department of Mathematics , Near East University , Nicosia, TRNC, Mersin 10, Turkey .

Abstract

Abstract Sturm-Liouville operator with second kind of nonlocal boundary value conditions is considered. For the classical solution, a priori estimate is established and unique existence is proved. Associated finite-difference scheme is proposed on uniform mesh and second-order accuracy for approximation is proved. An application of obtained results to nonlocal boundary problems with weight integral conditions is provided.

Publisher

Walter de Gruyter GmbH

Reference19 articles.

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2. [2] A. Sommerfeld, Ein Beitrag zur hydrodynamische Erklärung der turbulenten Flüssigkeitsbewegungen, Proceedings of the 4th International Congress of Mathematicians, Vol. III, 116-124 (In German).

3. [3] R. von Mises, Beitrag zum Oszillationsproblem, in Festschrift H. Weber, Teubner, Leipzig, 1912, 252-282 (In German).

4. [4] J. D. Tamarkin, I. On some general problems in the theory of ordinary linear differential equations and on the expansion in series of arbitrary functions, Petrograd, 1917 (In Russian).

5. [5] A. V. Bisadze and A. A. Samarskii, On some simple generalizations of linear elliptic boundary problems, USSR Academy of Science Reports 185(4) (1969), 739-740.

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