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Periodic solutions of nth order delay Rayleigh equations

Gen-Qiang Wang, Sui Sun Cheng (2002)

Annales Polonici Mathematici

A priori bounds are established for periodic solutions of an nth order Rayleigh equation with delay. From these bounds, existence theorems for periodic solutions are established by means of Mawhin's continuation theorem.

Positivity of Green's matrix of nonlocal boundary value problems

Alexander Domoshnitsky (2014)

Mathematica Bohemica

We propose an approach for studying positivity of Green’s operators of a nonlocal boundary value problem for the system of n linear functional differential equations with the boundary conditions n i x i - j = 1 n m i j x j = β i , i = 1 , , n , where n i and m i j are linear bounded “local” and “nonlocal“ functionals, respectively, from the space of absolutely continuous functions. For instance, n i x i = x i ( ω ) or n i x i = x i ( 0 ) - x i ( ω ) and m i j x j = 0 ω k ( s ) x j ( s ) d s + r = 1 n i j c i j r x j ( t i j r ) can be considered. It is demonstrated that the positivity of Green’s operator of nonlocal problem follows from the positivity of Green’s operator...

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