A Uniqueness Theorem for Beltrami 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.

Generalized Uniqueness Theorem for Ordinary Differential Equations in Banach Spaces

We consider nonlinear ordinary differential equations in Banach spaces. Uniqueness criterion for the Cauchy problem is given when any of the standard dissipative-type conditions does apply. A similar scalar result has been studied by Majorana (1991). Useful examples of reflexive Banach spaces whose positive cones have empty interior has been given as well.

Uniqueness Theorem for Ordinary Differential Equations with Hölder Continuity

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.