Positive Periodic Solutions in Shifts δ ± for a Class of Higher-Dimensional Functional Dynamic Equations with Impulses on Time Scales

Abstract EN

Let T ⊂ R be a periodic time scale in shifts δ ± with period P ∈ ( t 0 , ∞ ) T and t 0 ∈ T is nonnegative and fixed.

By using a multiple fixed point theorem in cones, some criteria are established for the existence and multiplicity of positive solutions in shifts δ ± for a class of higher-dimensional functional dynamic equations with impulses on time scales of the following form: x Δ ( t ) = A ( t ) x ( t ) + b ( t ) f ( t , x ( g ( t ) ) ) , t ≠ t j , t ∈ T , x ( t j + ) = x ( t j - ) + I j ( x ( t j ) ) , where A ( t ) = ( a i j ( t ) ) n × n is a nonsingular matrix with continuous real-valued functions as its elements.

Finally, numerical examples are presented to illustrate the feasibility and effectiveness of the results.