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General Periodic Boundary Value Problem for Systems

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DOI: 10.4236/am.2012.38130    4,231 Downloads   6,720 Views  
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ABSTRACT

The paper deals with the existence of nonzero periodic solution of systems, where k∈(0, π/T), α, β are n×n real nonsingular matrices, μ=(μ1…μn), f(t, u)=(f1(t, u),…,fn(t, u))∈C([0, T]×□n+,□+) 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 λ1 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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

M. Elnagi, "General Periodic Boundary Value Problem for Systems," Applied Mathematics, Vol. 3 No. 8, 2012, pp. 882-887. doi: 10.4236/am.2012.38130.

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