%0 Journal Article
%T General Periodic Boundary Value Problem for Systems
%A Mohammed Elnagi
%J Applied Mathematics
%P 882-887
%@ 2152-7393
%D 2012
%I Scientific Research Publishing
%R 10.4236/am.2012.38130
%X The paper deals with the existence of nonzero periodic solution of systems, where k¡Ê(0, ¦Ð/T), ¦Á, ¦Â are n¡Án real nonsingular matrices, ¦Ì=(¦Ì<sub>1</sub>¡­¦Ì<sub>n</sub>), f(t, u)=(f<sub>1</sub>(t, u),¡­,f<sub>n</sub>(t, u))¡ÊC([0, T]¡Á¡õ<sup>n</sup><sub>+</sub>,¡õ<sub>+</sub>) is periodic of period T in the t variable are continuous and nonnegative functions. We determine the Green¡¯s function and prove that the existence of nonzero periodic positive solutions if one of . In addition, if all i=£¨1¡­n£©where ¦Ë<sub>1</sub> is the principle eigenvalues of the corresponding linear systems. The proof based on the fixed point index theorem in cones. Application of our result is given to such systems with specific nonlinearities.
%K Systems
%K Principle Eigenvalues
%K Positive Solutions
%K Green¡¯s Function
%K Fixed Point Index Theorem in Cones
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=21481