Solvability of impulsive partial neutral second-order functional integro-differential equations with infinite delay

Abstract

Using the Kuratowski measure of noncompactness and progressive estimation method, we obtain the existence results of mild solutions for impulsive partial neutral second-order functional integro-differential equations with infinite delay in Banach spaces. The compactness condition of the impulsive term, some restrictive conditions on a priori estimation and noncompactness measure estimation have been deleted. Our conditions are simple and our results essentially improve and extend some known results. As applications, some examples are provided to illustrate the obtained results. MSC: 34K30; 34K40; 35R10; 47D09

Existence results of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay

“…Two examples are given in Section 4. Our results are based on the properties of equicontinuous semigroups and the ideas and techniques in Xie [24].…”

Stability of a thermoelastic laminated system subject to a neutral delay

“…Time delays are present in many problems and cannot be ignored even if they are small as they can affect drastically the structures. This is why they have been studied extensively the last three decades (see previous studies [1][2][3][4][5] ). In addition to the well-known discrete delays, there are several others and we are interested here in the neutral delay where the delay is occurring in the second (highest) derivative, for more details, see previous studies [6][7][8][9][10][11][12][13][14][15][16] and the references therein.…”

Stability for the damped wave equation with neutral delay

“…The existence and uniqueness of a mild solution for this type of problems has been discussed in , , , . It is proved in a more general abstract problems for an operator A generalizing the Laplacian, with domain: the set of functions v such that are absolutely continuous with Dirichlet boundary conditions.…”

“…Propagation and transmission of energy, material or information frequently embrace time delays [6], [7], [14][15][16], [20][21][22][23], [31], [37][38][39][40][41][42][43][44][45]. They used to be ignored in the past, but not nowadays.…”

“…Inside the class of FDEs, we distinguish those in which the time-delay appears in the derivatives as well. They are known as "Neutral Delay Differential Equations" (NDDEs) [2], [6][7][8][9], [11], [15], [16], [20], [22], [30], [37][38][39][40][41][42][43][44][45]. We can find them in the study of heat exchanges, control theory, biology, biosciences, in electric networks of high speed computers where the lossless transmission lines are used to interconnect switching circuits and in population ecology [1], [15][16][17][18][19][20], [23], [29], [41][42][43].…”