Geodesic
On second order periodic boundary-value problems with upper and lower solutions in the reversed order
Electronic journal of differential equations, Tome 2006 (2006)
In this paper, we study the differential equation with the periodic boundary value

$\displaylines{ u''(t)=f(t, u(t), u'(t)),\quad t\in [0, 2\pi]\cr u(0)=u(2\pi), \quad u'(0)=u'(2\pi). }$

The existence of solutions to the periodic boundary problem above with appropriate conditions is proved by using an upper and lower solution method.
Classification : 34B15, 34B16
Keywords: periodic boundary value, existence, upper and lower solutions 
@article{EJDE_2006__2006__a91,
     author = {Gao,  Haiyin and Weng,  Shiyou and Jiang,  Daqing and Hou,  Xuezhang},
     title = {On second order periodic boundary-value problems with upper and lower solutions in the reversed order},
     journal = {Electronic journal of differential equations},
     year = {2006},
     volume = {2006},
     zbl = {1096.34010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a91/}
}
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Gao,  Haiyin; Weng,  Shiyou; Jiang,  Daqing; Hou,  Xuezhang. On second order periodic boundary-value problems with upper and lower solutions in the reversed order. Electronic journal of differential equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a91/