Geodesic
On a criterion for the existence of at least four solutions of functional boundary value problems
Archivum mathematicum, Tome 33 (1997) no. 4, pp. 335-348.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

A class of functional boundary conditions for the second order functional differential equation $x''(t)=(Fx)(t)$ 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.
Classification : 47H15, 47N20
Keywords: functional boundary conditions; functional differential equation; existence; multiplicity; Bihari lemma; homotopy; Leray Schauder degree; Borsuk theorem 
@article{ARM_1997__33_4_a7,
     author = {Stan\v{e}k, Svatoslav},
     title = {On a criterion for the existence of at least four solutions of functional boundary value problems},
     journal = {Archivum mathematicum},
     pages = {335--348},
     publisher = {mathdoc},
     volume = {33},
     number = {4},
     year = {1997},
     mrnumber = {1601341},
     zbl = {0914.34063},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1997__33_4_a7/}
}
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
SP  - 335
EP  - 348
VL  - 33
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ARM_1997__33_4_a7/
LA  - en
ID  - ARM_1997__33_4_a7
ER  - 
%0 Journal Article
%A Staněk, Svatoslav
%T On a criterion for the existence of at least four solutions of functional boundary value problems
%J Archivum mathematicum
%D 1997
%P 335-348
%V 33
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ARM_1997__33_4_a7/
%G en
%F ARM_1997__33_4_a7
Staněk, Svatoslav. On a criterion for the existence of at least four solutions of functional boundary value problems. Archivum mathematicum, Tome 33 (1997) no. 4, pp. 335-348. http://geodesic.mathdoc.fr/item/ARM_1997__33_4_a7/