Existence of solution to nonlinear boundary value problem for ordinary differential equation of the second order in Hilbert space
Mathematica Bohemica (1992)
- Volume: 117, Issue: 4, page 415-424
- ISSN: 0862-7959
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topRovderová, Eva. "Existence of solution to nonlinear boundary value problem for ordinary differential equation of the second order in Hilbert space." Mathematica Bohemica 117.4 (1992): 415-424. <http://eudml.org/doc/29213>.
@article{Rovderová1992,
abstract = {In this paper we deal with the boundary value problem in the Hilbert space. Existence of a solutions is proved by using the method of lower and upper solutions. It is not necessary to suppose that the homogeneous problem has only the trivial solution. We use some results from functional analysis, especially the fixed-point theorem in the Banach space with a cone (Theorem 4.1, [5]).},
author = {Rovderová, Eva},
journal = {Mathematica Bohemica},
keywords = {boundary value problem; existence of solutions; ordinary differential equations in Hilbert space; lower and upper solution; boundary value problem; existence of solutions; ordinary differential equations in Hilbert space; lower and upper solution},
language = {eng},
number = {4},
pages = {415-424},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence of solution to nonlinear boundary value problem for ordinary differential equation of the second order in Hilbert space},
url = {http://eudml.org/doc/29213},
volume = {117},
year = {1992},
}
TY - JOUR
AU - Rovderová, Eva
TI - Existence of solution to nonlinear boundary value problem for ordinary differential equation of the second order in Hilbert space
JO - Mathematica Bohemica
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 117
IS - 4
SP - 415
EP - 424
AB - In this paper we deal with the boundary value problem in the Hilbert space. Existence of a solutions is proved by using the method of lower and upper solutions. It is not necessary to suppose that the homogeneous problem has only the trivial solution. We use some results from functional analysis, especially the fixed-point theorem in the Banach space with a cone (Theorem 4.1, [5]).
LA - eng
KW - boundary value problem; existence of solutions; ordinary differential equations in Hilbert space; lower and upper solution; boundary value problem; existence of solutions; ordinary differential equations in Hilbert space; lower and upper solution
UR - http://eudml.org/doc/29213
ER -
References
top- V. Šeda, On some non-linear boundary value problems for ordinary differential equations, Archivum Mathematicum (Brno) 25 (1989), 207-222. (1989) MR1188065
- B. Rudolf, Periodic boundary value problem in Hilbert space for differential equation of second order with reflection to the argument, Mathematica Slovaca 42 no. 1 (1992), 65-84. (1992) MR1159492
- M. Greguš M. Švec V. Šeda, Ordinary differential equations, Alfa, Bratislava, 1985. (In Slovak.) (1985)
- G. J. Šilov, Mathematical analysis, (Slovak translation), Alfa, Bratislava, 1985. (1985)
- M. A. Krasnosel'skij, Positive solutions of operators equations, Gosud. izd., Moskva, 1962. (In Russian.) (1962)
- E. Rovderová, A note on a Cone in the space , Diploma Thesis, 1990. (1990)
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