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Three periodic solutions for a class of higher-dimensional functional differential equations with impulses

Yongkun Li;  Changzhao Li;  Juan Zhang — 2010

Annales Polonici Mathematici

By using the well-known Leggett–Williams multiple fixed point theorem for cones, some new criteria are established for the existence of three positive periodic solutions for a class of n-dimensional functional differential equations with impulses of the form ⎧y’(t) = A(t)y(t) + g(t,yt), t ≠ t j , j ∈ ℤ, ⎨ ⎩ y ( t ⁺ j ) = y ( t ¯ j ) + I j ( y ( t j ) ) , where A ( t ) = ( a i j ( t ) ) n × n is a nonsingular matrix with continuous real-valued entries.

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