Almost-periodic solutions of nonlinear impulse systems

Almost Periodic Solutions of Evolution Differential Equations with Impulsive Action

“…Then these results were included in the well-known monograph [18]. Today there are many articles related to the study of almost periodic impulsive systems ( see, for example, [1,2,3,12,13,15,21,22,24]). In the papers [8,23,27,28] almost periodic solutions for abstract impulsive differential equations in the Banach space are investigated.…”

Almost periodic solutions of differential equations with piecewise constant argument of generalized type

“…Denote m 0 = max(m (2) , m (4) ) and define a representativeγ (2) of θ (2) with multiplicity m(i) = m 0 , i ∈ Z. Enlarging, if necessary, the multiplicity of elements and shifting the indeces of elements by the same number, in accordance with the change from γ (2) to γ (4) , we can construct representa-…”

“…Let γ (1) , γ (3) be the representatives of θ (1) , θ (3) , respectively, and γ (2) , γ (4) be the representatives of θ (2) such that ||γ…”

“…To solve the problems of the present paper, we intend to apply our knowledge about the almost periodicity of discontinuous solutions of impulsive systems [3]- [5], [17,31,34]. One should not be surprised with the relation between EPCAG and impulsive differential equations.…”

“…Following these results, in [4] we introduced Bohner type discontinuous almost periodic functions using topology as well as metric, in the spaces of discontinuous functions and in the discrete spaces of sets of points on the real axes, unbounded on the left and on the right. The multiplicity of one for the elements of the sets was mentioned there, since we supposed that the distances between neighbors are uniformly separated from zero.…”