Please use this identifier to cite or link to this item:https://hdl.handle.net/20.500.12259/36142
Type of publication: Magistro darbas / Master thesis
Field of Science: Matematika / Mathematics
Author(s): Vitkauskaitė, Vilma
Title: Uždavinio su nelokaliąja integraline sąlyga Fučiko spektro tyrimas
Other Title: Investigation of Fučik Type Spectrum for Problem with Nonlocal Integral Condition
Extent: 27 p.
Date: 21-May-2018
Event: Vytauto Didžiojo universitetas. Informatikos fakultetas. Matematikos ir statistikos katedra
Keywords: Fučiko uždavinys;Fučiko lygtis;Spektras;Integralinė nelokalioji sąlyga;Fučik problem;Fučik equation;Spectrum;Integral nonlocal condition
Abstract: Šiame magistriniame darbe nagrinėjama Fučiko lygties x 00 = −µx + + λx − su vienaklasikine x (0) = 0 , o kita nelokaliąja integraline kraštine sąlyga R ξ 0 x ( s ) dt = 0 , spektro priklausomybė nuo nelokaliosios sąlygos parametrų γ ir ξ. Išsamiai ištirtas atvejis, kai ξ = 1/4. Pirmajame baigiamojo darbo skyriuje suformuluotas Fučiko uždavinys. Antrajame skyriuje aprašyta Fučiko lygties spektro tyrimo metodika bei Fučiko lygties su klasikinėmis kraštinėmis sąlygomis spektras. Taip pat šiame skyriuje, vadovaujantis aukščiau aprašyta metodika, išnagrinėtas Fučiko lygties spektras, kai nelokaliosios sąlygos parametras ξ = 1 / 4. Magistriniame darbe pateiktos analizinės spektro išraiškos ir grafikai su tam tikromis parametro γ reikšmėmis.
In the master thesis the Fučik equation x 00 = −µx + + λx − , with one classical x (0) = 0 and with another nonlocal integral boundary condition R ξ 0 x ( s ) dt = 0 is analysed. Condi-tion parameters γ and ξ are investigated as well as dependence of the Fučik spectrum on nonlocal boundary. The case when ξ = 1/4 is analyzed in greater detail. The first chapter of this thesis contains formulation of the Fučik problem. In the second chapter the investigation methodology of spectrum of the Fučik equation and the spectrum of the Fučik equation with classical boundary conditions are described. Furthermore, this chapter includes analysis of the spectrum of the Fučik equation when nonlocal condition parameter ξ = 1 / 4 based on the above described methodology. In the final thesis the analytical expressions and graphs of spectrum with certain meanings of the parameter γ are presented.
Internet: https://hdl.handle.net/20.500.12259/36142
Appears in Collections:2018 m. (IF mag.)

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