The main aim of this paper is to develop some basic theories of neutral stochastic functional differential equations (NSFDEs). Firstly, we establish a local existenceuniqueness theorem under the local ...

The first part of the paper deals with an infinite system of weakly coupled (this means that every equation contains derivatives of only one unknown function ...

Liouville theorems have long been a cornerstone in the study of partial differential equations, offering fundamental insights into the nonexistence of non-trivial solutions under specific growth or ...

Elliptic equations play a central role in the study of steady-state phenomena across physics, engineering and geometry. Their analysis not only provides insights into the qualitative behaviour of ...