General Periodic Boundary Value Problem for Systems

Mohammed Elnagi

Department of Mathematics, Faulty of Educations, Khartoum University, Omdurman, Sudan.

DOI: 10.4236/am.2012.38130                

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…μ_n), f(t, u)=(f₁(t, u),…,f_n(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.

Keywords

Systems; Principle Eigenvalues; Positive Solutions; Green’s Function; Fixed Point Index Theorem in Cones

Conflicts of Interest

The authors declare no conflicts of interest.

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