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Periodic solutions for some fully nonlinear fourth order differential equations
1.  Departamento de Matemática. Universidade de Évora, Centro de Investigação em Matemática e Aplicaçoes da U.E. (CIMAUE), Rua Romão Ramalho, 59. 7000671 Évora 
$u^((i))(a) = u^((i))(b), i=0,1,2,3,$
The difficulties in the odd derivatives are overcome due to the following arguments: the control on the third derivative is done by a Nagumotype condition and the bounds on the first derivative are obtained by lower and upper solutions, not necessarily ordered.
By this technique, not only it is proved the existence of a periodic solution, but also, some qualitative properties of the solution can be obtained.
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