A UNIFIED EXISTENCE AND UNIQUENESS THEOREM FOR STOCHASTIC EVOLUTION EQUATIONS

A Unified Existence and Uniqueness Theorem for Stochastic Evolution Equations

An existence and uniqueness theorem for mild solutions of stochastic evolution equations is presented and proved. The diffusion coefficient is handled in a unified way which allows a unified theorem to be formulated for different cases, in particular, of multiplicative space–time white noise and trace-class noise. 2000 Mathematics subject classification: primary 60H15; secondary 35K90.

Existence and uniqueness theorem for uncertain differential equations

Canonical process is a Lipschitz continuous uncertain process with stationary and independent increments, and uncertain differential equation is a type of differential equations driven by canonical process. This paper presents some methods to solve linear uncertain differential equations, and proves an existence and uniqueness theorem of solution for uncertain differential equation under Lipsch...

Existence and Uniqueness Theorem for Uncertain Delay Differential Equations ?

Uncertain delay differential equation is a type of functional differential equations driven by canonical process. This paper presents a method to solve an uncertain delay differential equation, and proves an existence and uniqueness theorem of solution for uncertain delay differential equations under Lipschitz condition and linear growth condition by Banach fixed point theorem.

Existence and Uniqueness Theorem for Stochastic Differential Equations with Self-Exciting Switching

Existence and uniqueness results for a nonlinear differential equations of arbitrary order

This paper studies a fractional boundary value problem of nonlinear differential equations of arbitrary orders. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using Schaefer and Krasnoselskii fixed point theorems. In order to clarify our results, some illustrative examples are also presented.