- Tytuł:
- Application of Greens operator to quadratic variational problems
- Autorzy:
-
Azbelev, N. V.
Tsalyuk, V. Z. - Powiązania:
- https://bibliotekanauki.pl/articles/255629.pdf
- Data publikacji:
- 2006
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
quadratic variational problem
Sobolev space
boundary value problem
Hilbert space
Green's operator
Fredholm integral operator
spectrum - Opis:
- We use Green's function of a suitable boundary value problem to convert the variational problem with quadratic functional and linear constraints to the equivalent unconstrained extremal problem in some subspace of the space L2 of quadratically summable functions. We get the neccessary and sufficient criterion for unique solvability of the variational problem in terms of the spectrum of some integral Hilbert-Schmidt operator in L2 with symmetric kernel. The numerical technique is proposed to estimate this criterion. The results are demonstrated on examples: 1) a variational problem with deviating argument, and 2) the problem of the critical force for the vertical pillar with additional support point (the qualities of the pillar may vary discontinuously along the pillar's axis).
- Źródło:
-
Opuscula Mathematica; 2006, 26, 2; 243-256
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł