Nonlinear Integro-Differential Equations in Banach Spaces

Existence and regularity of solutions for some partial functional integrodifferential equations in Banach spaces

We are concerned with fractional Sobolev-type integro-differential equations in Banach spaces with operator pairs and impulsive conditions, where the operator pairs generate propagation families. With the help of the theory of propagation family and Laplace transforms, along with an estimate for a special sequence improved in this article, we introduce a definition of mild solutions to the impulsive problem for these abstract fractional Sobolev-type integro-differential equations and we establish general existence theorems and a continuous dependence theorem, which essentially extend some previous conclusions. In our results, the operator B could be unbounded, and the existence of an operator B−1 is not necessarily needed. Moreover, we give some examples to illustrate our main results.

Multiple positive solutions of a boundary value problem for nth-order impulsive integro-differential equations in Banach spaces

In this paper, we prove the existence of solutions of initial value problems for nth order nonlinear impulsive integro-differential equations of mixed type on an infinite interval with an infinite number of impulsive times in Banach spaces. Our results are obtained by introducing a suitable measure of noncompactness.

In this paper we establish the existence of a unique classical solution to a class of quasilinear integrodifferential equations in a general Banach space.

This paper defines a concept of a semi-k-set-contraction operator, and establishes a degree theory for it. As its application, we discuss the existence for the solution of two-point boundary value problems for nonlinear second order integro-differential equations in Banach spaces.

The Study aims in this paper to give and investigate the existence and uniqueness of mild solutions to nonlinear functional integrodifferential equations in Banach Spaces. the fixed point theorem, according to Sadovskii and sutible necessary conditions, are concepts consulted to obtain the results in the work

This paper studies fractional differential equations (FDEs) with mixed fractional derivatives. Existence, uniqueness, stability, and asymptotic results are derived.

In this paper we study the existence of mild solutions for a class of first-order delay integrodifferential equations with nonlocal condition in a Banach space.The results are established by the application of the theory of resolvent operators, the contraction mapping principle and the Schaefer theorem.An example is presented in the end to show the applications of the obtained results.

This paper focuses on the existence of mild solutions in Banach space for a first order semi-linear integro-differential equation. The results are achieved with the fixed-point theorem and Kuratowski measure of noncompactness. We conclude this study with an example to illustrate our findings.

SummaryIn this work, we study the existence and stability of solutions for an optimal control problem governed by an integrodifferential equation with compact control set in the space L1([0,b];X). The stability results, in the sense of Baire category theory, for optimal control problems are obtained by the theory of set‐valued mapping and the notion of essential solutions for optimal control problems.

This paper deals with inverse problems related to degenerate fractional integro-differential equations in Banach spaces. We study existence, uniqueness and regularity of solutions to the problem, claiming to extend well known studies for the case of non-fractional equations. Our method is based on transforming the inverse problem to a direct problem and identifying the conditions under which this direct problem has a unique solution. The conditions under which the unique strict solution can be compared with the case of a mild solution, obtained in previous studies under quite restrictive requirements, are on the underlying functions. Applications from partial differential equations are given to illustrate our abstract results.

Sufficient conditions are established for the existence\nresults of\nfractional order semilinear Volterra integrodifferential equations\nin Banach spaces. Results are obtained by using the theory of\nfractional cosine families and fractional powers of operators.

On the stability and asymptotic behavior of solutions of integrodifferential equations in Banach spaces

In the present paper, we investigate the global existence of solutions to initial value problem for nonlinear mixed Volterra–Fredholm functional integrodifferential equations in Banach spaces. The technique used in our analysis is based on an application of the topological transversality theorem known as Leray–Schauder alternative and rely on a priori bounds of solution.