In this article, we study the existence and uniqueness of solutions for Hadamard-type sequential fractional order neutral functional differential equations. The Banach fixed point theorem, a nonlinear alternative of LeraySchauder type and Krasnoselski fixed point theorem are used to obtain the desired results. Examples illustrating the main results are presented. An initial value integral condi...

In this paper, we introduce six axioms for relative Bott-Chern secondary characteristic classes and prove the uniqueness and existence theorem for them. Such a work provides us a natural way to understand and hence to prove the arithmetic Grothendieck-Riemann-Roch theorem.

In this paper, we prove a theorem on local existence and uniqueness of integral solutions to a class of partial neutral functional differential equations with infinite delay. Our method of proof is based on the integrated semigroup theory and the well known Banach fixed point theorem.

We consider existence and uniqueness of two kinds of coisotropic embeddings and deduce the existence of deformation quantizations of certain Poisson algebras of basic functions. First we show that any submanifold of a Poisson manifold satisfying a certain constant rank condition, already considered by Calvo and Falceto (2004), sits coisotropically inside some larger cosymplectic submanifold, wh...

We prove existence and uniqueness of the solution of a parabolic SPDE in one space dimension driven by space-time white noise, in the case of a measurable drift and a constant diffusion coefficient, as well as a comparison theorem.

a consistency criteria is given for a certain class of finite positive measures on the surfaces of the finite dimensional unit balls in a real separable hilbert space. it is proved, through a kolmogorov type existence theorem, that the class induces a unique positive measure on the surface of the unit ball in the hilbert space. as an application, this will naturally accomplish the work of kante...

The Banach fixed point theorem and a nonlinear alternative of Leray-Schauder type are used to investigate the existence and uniqueness of solutions for fractional order Hadamard-type functional and neutral functional differential equations.

A local theorem of existence and uniqueness of solutions of the equations of stationary axially symmetric vacuum gravitational fields in the general theory of relativity close to the flat space solution is proved using the implicit function theorem in Banach spaces. Mathematics Subject Classification (2010). 83C10, 83C05

In this paper we investigate the existence and uniqueness of solutions of a class of partial impulsive hyperbolic differential equations with fixed time impulses involving the Caputo fractional derivative. Our main tool is a fixed point theorem.

In this paper, the comparison theorem of stochastic differential delay equations with Markovian switching has been investigated. In order to develop our theory, a new proof of existence and uniqueness of stochastic differential equations with Markovian switching is given.