Abstract We study a nonautonomous semilinear parabolic problem with dynamical boundary condition in an irregular domain fractal boundary. Local existence, uniqueness and regularity results for the mild solution are established via family of evolution operators. A sufficient on initial datum global existence is given.

We study the problem of estimating the mean of a multivariate distribution based on independent samples. The main result is the proof of existence of an estimator with a non-asymptotic sub-Gaussian performance for all distributions satisfying some mild moment assumptions.

This paper gives a proof of existence of price equilibria under certain parameters for a model of product differentiation commonly used in the empirical geographic differentiation literature. This proof is needed because the assumptions of Caplin and Nalebuff (1991) are not generally satisfied once data is introduced to geographic models. The theorem also has implications for existence in mixed...

In this paper, we consider a mechanochemical model in biological patterns $ \mathbb{R}^N $, N\geq 5 $. We first prove the existence of time periodic solution BC(\mathbb{R}; L^{N,\infty}(\Omega)) Then obtain existence, uniqueness and regularity mild problem. Finally, that can become strong

in this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in banach spaces admitting the existence of a lower solution.

in his recognition of being and achievement of truth, man has two instruments in his constitution and two ways before him: intellect and heart; reasoning and intuition. some have opted the way of reasoning and underestimated intuition because of its lack of reasoning, and some have preferred intuition over reasoning because of its being presential (intuitive). with their research on philosophy ...

in this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in banach spaces admitting the existence of a lower solution.