In this paper a stochastic differential equation (SDE) with infinite memory is considered. The drift coefficient of the equation is a nonlinear functional of the past history of the solution. Sufficient conditions for existence and uniqueness of stationary solution are given. This work is motivated by recent papers [1] and [2] where stochastically forced nonlinear equations of hydrodynamics wer...

Inspired by the fact that the discontinuous mappings cannot be (Banach type) contractions and cyclic contractions need not be continuous, and taking into account that there are applications to integral and differential equations based on cyclic contractions, a new type of cyclic contraction mappings satisfying an implicit relation that involves a control function for a map in a metric space is ...

In this paper, we are concerned with the study of mathematical analysis for an optimal control a nonlocal degenerate aggregation model. This model describes organisms such as pedestrian movements, chemotaxis, animal swarming. We establish wellposedness (existence and uniqueness) weak solution direct problem by means auxiliary nondegenerate equation, Faedo–Galerkin method (for existence result) ...