arXiv subjects

Mohammad Niksirat

Publications and source records attributed to Mohammad Niksirat.

3 recordsLinked to original sources

arXiv2019

A new generalization of Browder degree

A new generalization of the Browder's degree for the mappings of the type $(S)_+$ is presented. The main idea is rooted in the observation that the Browder's degree remains unchanged for the mappings of the form $A: Y\to X^*$, where $Y$ is a reflexive uniformly convex Banach space continuously embedded in the Banach space $X$. The advantage of the suggested degree lies in the simplicity it provides for the calculations of the degree associated with nonlinear operators. An application from the theory of phase transition in liquid crystals is presented for which the suggested degree has been successfully applied.

math.AP↗

arXiv2019

A new construction of the degree of maximal monotone maps

The inclusion equations of the type $f \in T ( x)$ where $T: X \to 2^{X^{\ast}}$ is a maximal monotone map, are extensively studied in nonlinear analysis. In this paper, we present a new construction of the degree of maximal monotone maps of the form $T: Y \to 2^{X^*}$, where $Y$ is a locally uniformly convex and separable Banach space continuously embedded in the uniformly convex Banach space $X$. The advantage of the new construction lies in the remarkable simplicity it offers for calculation of degree in comparison with the classical one suggested by F. Browder. We prove a few classical theorems in convex analysis through the suggested degree.

math.AP↗

arXiv2018

On the stationary solutions of Doi-Onsager model in general dimension

We give new results of the phase transition of dilute colloidal solutions of rod-like molecules in dimension $D \geq 3$. For the low concentration of particles in a carrier fluid, we prove that the isotropic phase is the unique solution to the Doi-Onsager model with the general potential kernel. In addition, we present the regime of the bifurcation of nematic phases in the class of axially symmetric solutions. Our method is based on a generalization of the classical Leray-Schauder degree we developed for this problem.

math.AP↗