We construct a family of vertex transitive graphs on a left loop structure of order 2q2 where q is a power of a prime such that q equivalent to 1 mod 4. The graphs are of diameter 2. The smallest of these graphs is isomorphic to the Hoffman-Singleton graph.
We present a comprehensive analysis of the existence and regularity of distributional solutions for a given class of nonlinear degenerate elliptic equations. The equations under consideration contain singular gradient lower order terms and are related to the L(m )data, where the exponent m satisfies 1 < m < d/p(-). To deal with this problem, we use a functional framework that includes Lebesgue-Sobolev spaces with variable exponents. Our findings provide valuable additions to the previous research discussed in Nonlinear degenerate p(x)-Laplacian equation with singular gradient and lower order term (2023) by H. Khelifi and M. A. Zouatini.
The statistical convergence in a topological space is constrained in this study up to order alpha, where alpha is an element of (0, 1). A fresh group of open covers (namely s-gamma covers) and an entirely novel category of denseness (namely s-denseness) are proposed using this notion of s-convergence, which has been used to study various topological aspects of s-density. It has been revealed that the class of s-gamma coverings falls somewhere between the class of gamma covers and the class of s-gamma covers. The influence of s-gamma covers in topological games and selection principles are also investigated.
Under weak conditions on the diffusion coefficients, we prove existence theorems of weak solutions for some nonlinear nonlocal elliptic problems. Our approach is based on the Schauder fixed point theorem combined with an approximation technique. We also give uniqueness results and an example to support them.
