Existence results for some partial integrodifferential equations with nonlocal conditions

Abstract

Abstract. In this work, we study the existence of mild solutions for a class of partial integrodifferential equations with nonlocal conditions. Our analysis uses the resolvent operator theory and relies on a new fixed point theorem of Sadovskii-Krasnosel'skii type. Our results improve and complement several earlier related works. Some examples are provided to illustrate the theoretical results.

Existence of solutions for some functional integrodifferential equations with nonlocal conditions

“…Many authors derived the existence and uniqueness of solutions by using the resolvent operator technique. [4][5][6][7] From their results, they gave more important to nonlocal initial condition problems because it has more realistic than the classical one, especially in physical problems, see previous studies. [8][9][10][11] The field of differential calculus has many real-world applications in various fields of science and engineering.…”

“…[24][25][26][27][28][29] In this paper, we approach a new technique, that is, g is not compactness and using iterative methods based on the Sadovskii-Krasnosel'skii type of fixed point theorem technique in Ezzinbi et al 30 and to show that immediate norm continuity of R 1 (t 1 ) associated to (1.1) is to the semigroup T(t) is immediate norm continuity. Motivated by the above mentioned articles, 6,7,[16][17][18]30 the purpose of this paper is to study the existence of solutions for some functional integrodifferential equations with nonlocal conditions (1.1) and (1.2). Throughout, this analysis used the concept of fixed point technique of Sadovskii's type and resolvent operator.…”

“…The problem of existence and uniqueness of solutions of the special form as in () have been discussed by many authors with their distinct techniques. Many authors derived the existence and uniqueness of solutions by using the resolvent operator technique 4‐7 . From their results, they gave more important to nonlocal initial condition problems because it has more realistic than the classical one, especially in physical problems, see previous studies 8‐11 …”

Stability for some impulsive neutral stochastic functional integro-differential equations driven by fractional Brownian motion

“…Theorem 2.8. (Ezzinbi et al, 2016). Let Ξ be the infinitesimal generator of a C 0 -semigroup ðSðtÞÞ t � 0 and let ðΘðtÞÞ t � 0 satisfies (P2).…”

A Study on the Impact of Nonlinear Source Term in Black-Scholes Option Pricing Model

“…In [11,12], the authors adopted fixed-point technique in the discussion on the existence of various forms of solution of an almost periodic stochastic differential equations. The works in [13][14][15] studied the existence of solutions for PDE under nonlocal conditions. Moreover, the works in [16][17][18][19][20] also deals with the different forms of Black-Scholes equation and studied the existence theory.…”