Using a suitable version of Mawhin’s continuation principle, we obtain an existence result for the Floquet boundary value problem for second order Carathéodory differential equations by means of strictly localized $ C^2 $ bounding functions.
@article{116926, author = {Valentina Taddei}, title = {Two-points boundary value problems for Carath\'eodory second order equations}, journal = {Archivum Mathematicum}, volume = {044}, year = {2008}, pages = {93-103}, zbl = {1212.34039}, mrnumber = {2432846}, language = {en}, url = {http://dml.mathdoc.fr/item/116926} }
Taddei, Valentina. Two-points boundary value problems for Carathéodory second order equations. Archivum Mathematicum, Tome 044 (2008) pp. 93-103. http://gdmltest.u-ga.fr/item/116926/
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