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 ...

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 ...

We prove a general criterion for the uniqueness of critical points of a functional in the presence of constraints such as positivity, boundedness, or fixed mass. Our method relies on convexity ...

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 ...