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.

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The paper presents the investigation of the impact of Ignalina Nuclear Power Plant (NPP) shutdown on Lithuanian energy security. The system of energy security indicators, covering technical, economic and socio-political aspects is presented. The integral characteristic of these indicators shows the level of energy security. The paper analyses the Lithuanian energy security level in 2007. To make a comparison, the energy security level in 2010, after the shutdown of Ignalina NPP, when Lithuanian Power Plant in Elektrėnai becomes the main electricity producer, is forecasted. Two alternatives are analysed: Lithuanian Power Plant uses either gas or heavy fuel oil for electricity production. The security level of each indicator, each indicator block and the total security level are presented as the result. Energy security indicators, which increased or decreased after the shutdown of Ignalina NPP, are analysed, including the indicators which have had the greatest impact on the change in energy security level. The influence of Ignalina NPP shutdown on CO2 emissions is presented. Also, electricity generating costs for different types of electricity production at a different discount rate are presented.

In this paper the Sturm-Liouville problem with one classical and the other nonlocal two-point or integral boundary condition is investigated. Critical points of the characteristic function are analyzed. We investigate how distribution of the critical points depends on nonlocal boundary condition parameters. In the first part of this paper we investigate the case of negative critical points.