Existence of solutions for neutral functional differential evolution equations with nonlocal conditions

Existence of a mild solution for an impulsive nonlocal non-autonomous neutral functional differential equation

“…In [25], authors have established the existence of mild solutions to a nonlocal impulsive integro-differential equations via measure of noncompactness and new fixed point theorem. By utilizing fixed point theorem for condensing operator and approximation techniques, the existence of the mild solution is obtained by authors in [26]. An impulsive neutral integro-differential equation of Sobolev type with time varying delays has been considered by authors in [27] and the sufficient condition for existence of the mild solution has been provided by using the Monch's fixed point theorem.…”

“…In [17], authors have concerned with the existence of α-mild solutions for a fractional stochastic integro-differential equations with nonlocal initial conditions in a real separable Hilbert space by using an approximation technique. For more details, we refer to papers [11,[14][15][16][17][18][19][20]24,26,28] and references given therein.…”

“…For more details on non-autonomous differential equations, we refer to monograph [21,22], and papers [1][2][3][4][5][6][7][8]11,12,26,27,[29][30][31][32][33][34][35] and references cited therein.…”

On the evolution differential inclusions under a noncompact evolution system

“…Then it has been studied extensively under various conditions, see [3,4,7,8,13,14,21]. Byszewski and Lakshmikantham [9] obtained the existence and uniqueness of mild solutions in the case that Lipschitz-type conditions are satisfied.…”

Existência de soluções para equações integro-diferenciais neutras

“…Em relação a sistemas abstratos do tipo neutro de primeira ordem modelados como (3)- (4) ou (7)- (8) citamos entre outros trabalhos, [2,3,4,5,22,33,45,46] para existência de soluções fracas; [5,45] para regularidade de soluções fracas; [2] para estabilidade de soluções; [32,35,34] para existência de soluções periódicas; [36] para a existência de soluções quase e assintoticamente quase periódicas; [37,38,39] para soluções pseudo quase periódicas; [40,41] para sistemas impulsivos e [22,43] para sistemas com condições não locais.É interessante citar também [46,42], onde são feitas algumas correções de recentes trabalhos tratando sobre a existência e controlabilidade exata de soluções associadas a sistemas do tipo neutro.…”