On a criterion for the existence of at least four solutions of functional boundary value problems
Archivum Mathematicum (1997)
- Volume: 033, Issue: 4, page 335-348
- ISSN: 0044-8753
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topStaněk, Svatoslav. "On a criterion for the existence of at least four solutions of functional boundary value problems." Archivum Mathematicum 033.4 (1997): 335-348. <http://eudml.org/doc/248037>.
@article{Staněk1997,
abstract = {A class of functional boundary conditions for the second order functional differential equation $x^\{\prime \prime \}(t)=(Fx)(t)$ is introduced. Here $F:C^1(J) \rightarrow L_1(J)$ is a nonlinear continuous unbounded operator. Sufficient conditions for the existence of at least four solutions are given. The proofs are based on the Bihari lemma, the topological method of homotopy, the Leray-Schauder degree and the Borsuk theorem.},
author = {Staněk, Svatoslav},
journal = {Archivum Mathematicum},
keywords = {functional boundary conditions; functional differential equation; existence; multiplicity; Bihari lemma; homotopy; Leray Schauder degree; Borsuk theorem; functional boundary conditions; functional-differential equations; existence; multiplicity; Bihari lemma; homotopy; Leray Schauder degree; Borsuk theorem},
language = {eng},
number = {4},
pages = {335-348},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On a criterion for the existence of at least four solutions of functional boundary value problems},
url = {http://eudml.org/doc/248037},
volume = {033},
year = {1997},
}
TY - JOUR
AU - Staněk, Svatoslav
TI - On a criterion for the existence of at least four solutions of functional boundary value problems
JO - Archivum Mathematicum
PY - 1997
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 033
IS - 4
SP - 335
EP - 348
AB - A class of functional boundary conditions for the second order functional differential equation $x^{\prime \prime }(t)=(Fx)(t)$ is introduced. Here $F:C^1(J) \rightarrow L_1(J)$ is a nonlinear continuous unbounded operator. Sufficient conditions for the existence of at least four solutions are given. The proofs are based on the Bihari lemma, the topological method of homotopy, the Leray-Schauder degree and the Borsuk theorem.
LA - eng
KW - functional boundary conditions; functional differential equation; existence; multiplicity; Bihari lemma; homotopy; Leray Schauder degree; Borsuk theorem; functional boundary conditions; functional-differential equations; existence; multiplicity; Bihari lemma; homotopy; Leray Schauder degree; Borsuk theorem
UR - http://eudml.org/doc/248037
ER -
References
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