1. CMB 2011 (vol 55 pp. 736)
|Existence of Solutions for Abstract Non-Autonomous Neutral Differential Equations |
In this paper we discuss the existence of mild and classical solutions for a class of abstract non-autonomous neutral functional differential equations. An application to partial neutral differential equations is considered.
Keywords:neutral equations, mild solutions, classical solutions
Categories:35R10, 34K40, 34K30
2. CMB 2010 (vol 53 pp. 526)
|On Some Stochastic Perturbations of Semilinear Evolution Equations|
We consider semilinear evolution equations with some locally Lipschitz nonlinearities, perturbed by Banach space valued, continuous, and adapted stochastic process. We show that under some assumptions there exists a solution to the equation. Using the result we show that there exists a mild, continuous, global solution to a semilinear ItÃ´ equation with locally Lipschitz nonlinearites. An example of the equation is given.
Keywords:evolution equation, mild solution, non-Lipschitz drift, Ito integral