TITLE:
General Periodic Boundary Value Problem for Systems
AUTHORS:
Mohammed Elnagi
KEYWORDS:
Systems; Principle Eigenvalues; Positive Solutions; Green’s Function; Fixed Point Index Theorem in Cones
JOURNAL NAME:
Applied Mathematics,
Vol.3 No.8,
August
1,
2012
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.