Green's Function and Existence of a Unique Solution for a Third-Order Three-Point Boundary Value Problem

The solutions of third-order three-point boundary value problem x"' + f (t,x) = 0, t [member of] [a,b], x(a) = x'(a) = 0, x(b) = kx([eta]), where [eta] [member of] (a,b), k [member of] R, f [member of] C([a,b] x R, R) and f (t, 0) [not equal to] 0, are the subject of this investigatio...

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Bibliographic Details
Published inMathematical modelling and analysis Vol. 24; no. 2; p. 171
Main Author Smirnov, Sergey
Format Journal Article
LanguageEnglish
Published Vilnius Gediminas Technical University 01.05.2019
Subjects
Basketball players
Boundary value problems
Existence theorems
Mathematical research
Potential theory (Mathematics)
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ISSN1392-6292
DOI10.3846/mma.2019.012

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Summary:The solutions of third-order three-point boundary value problem x"' + f (t,x) = 0, t [member of] [a,b], x(a) = x'(a) = 0, x(b) = kx([eta]), where [eta] [member of] (a,b), k [member of] R, f [member of] C([a,b] x R, R) and f (t, 0) [not equal to] 0, are the subject of this investigation. In order to establish existence and uniqueness results for the solutions, attention is focused on applications of the corresponding Green's function. As an application, also one example is given to illustrate the result. Keywords: Green's function, nonlinear boundary value problems, three-point boundary conditions, existence and uniqueness of solutions. AMS Subject Classification: 34B10; 34B15.
ISSN:1392-6292
DOI:10.3846/mma.2019.012