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http://hdl.handle.net/10174/3701
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Title: | Periodic solutions for some fully nonlinear fourth order differential equations |
Authors: | Minhós, Feliz |
Keywords: | Periodic solutions Fourth order nonlinear BVP |
Issue Date: | 2011 |
Abstract: | In this paper we present sufficient conditions for the existence of periodic
solutions to some nonlinear fourth order boundary value problems
u(4)(x) = f(x; u(x); u′(x); u′′(x); u′′′(x))
u(i)(a) = u(i)(b); i = 0; 1; 2; 3;
To the best of our knowledge it is the first time where this type of general nonlinearities is
considered in fourth order equations with periodic boundary conditions.
The difficulties in the odd derivatives are overcome due to the following
arguments: the control on the third derivative is done by a Nagumo-type
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. |
URI: | http://hdl.handle.net/10174/3701 |
Type: | article |
Appears in Collections: | CIMA - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica
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