STURM-LIOUVILLE PROBLEM FOR STATIONARY DIFFERENTIAL OPERATOR WITH NONLOCAL INTEGRAL BOUNDARY CONDITION
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Open Access
- 31 December 2005
- journal article
- Published by Vilnius Gediminas Technical University in Mathematical Modelling and Analysis
- Vol. 10 (4) , 377-392
Abstract
The Sturm‐Liouville problem with various types of nonlocal integral boundary conditions is considered in this paper. In the first part of paper we investigate Sturm‐Liouville problem with two cases of nonlocal integral boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such problem in the complex case. In the second part we investigate real eigenvalues case. The spectrum depends of these problems on boundary condition parameters is analyzed. Qualitative behaviour of all eigenvalues subject to nonlocal boundary condition parameters is described. Šiame straipsnyje nagrinejamas Šturmo‐Liuvilio uždavinys su viena nelokaliaja integralinio tipo kraštine salyga. Pirmoje straipsnio dalyje tiriamas Šturmo‐Liuvilio uždavinys su dvieju tipu integraline nelokaliaja salyga. Irodytos tikriniu funkciju ir tikriniu reikšmiu bendrosios savybes komplesineje plokštumoje. Antroje dalyje plačiau ištirtas realiuju tikriniu reikšmiu atvejis. Straipsnyje nagrinejama kaip Šturmo‐Liuvilio uždavinio spektras priklauso nuo kraštiniu salygu parametru. Priklausomai nuo nelokaliuju kraštiniu salygu parametru, aprašytas kokybinis tikriniu reikšmiu pasiskirstymas.Keywords
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