Related papers: Symmetry breaking results for problems with expone…
Symmetry is a common feature of many combinatorial problems. Unfortunately eliminating all symmetry from a problem is often computationally intractable. This paper argues that recent parameterized complexity results provide insight into…
A semilinear reaction-diffusion two-point boundary value problem, whose second-order derivative is multiplied by a small positive parameter $\eps^2$, is considered. It can have multiple solutions. An asymptotic expansion is constructed for…
In this paper we study the bifurcation of branches of non-symmetric solutions from the symmetric branch of solutions to the Euler-Lagrange equations satisfied by optimal functions in functional inequalities of Caffarelli-Kohn-Nirenberg…
We find numerical solutions of Einstein equations and scalar field equation for a global defect in higher dimensional spacetimes ($\geq 6$). We examine in detail the relation among the expansion rate $H$ and the symmetry-breaking scale…
In this paper, we will solve this uniqueness problem of positive solutions to the following equations of exponential growth: \begin{equation*} \begin{cases} -\Delta u =\lambda ue^{u^2},\quad\quad & x\in B_1\subset \mathbb{R}^2,\\ u>0, &…
To obtain a simple description of a geometrically thin magnetic accretion disk, we apply the method of asymptotic expansion. For the first time we write a full set of stationary asymptotic approximation equations of a thin magnetic…
In this article, we present the symmetry of weak solutions to a mixed local-nonlocal singular problem. We also establish results related to the existence, nonexistence, and regularity of weak solutions to a mixed local-nonlocal singular…
Asymptotic properties of certain arithmetic functions involving exponential divisors are investigated.
We obtain characterizations of nonuniform dichotomies, defined by general growth rates, based on admissibility conditions. Additionally, we use the obtained characterizations to derive robustness results for the considered dichotomies. As…
Accretion disks in close binary systems are subject to a tidally driven parametric instability which leads to the growth of internal waves near the outer edges of such disks (Goodman 1993). These waves are important in understanding the…
We review the results of our recent numerical investigations on the electronic properties of disordered two dimensional systems with chiral unitary, chiral orthogonal, and chiral symplectic symmetry. Of particular interest is the behavior…
A model of two coupled complex scalar fields is studied at finite temperature and under an external magnetic field. The results are obtained in the context of the nonperturbative method of the optimized perturbation theory and contrasted…
We study certain weighted area integral means of analytic functions in the unit disc. We relate the growth of these means to the property of being mean H\"older continuous with respect to the Bergman space norm. In contrast with earlier…
We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms, focussing on the case of multiple, non-commensurate frequencies. We derive an asymptotic expansion in inverse powers of the…
This work is devoted to the investigation of the problem about inverse mapping systems expansions of ultrauniform spaces $X$ using polyhedra over non-Archimedean locally compact fields $\bf L$. Theorems about expansions of complete…
This paper is devoted to discuss some of the features of self-similar solutions of the first kind. We consider the cylindrically symmetric solutions with different homotheties. We are interested in evaluating the quantities acceleration,…
We perform a linear stability analysis of the axisymmetric, relativistic, self-similar isothermal disk against non-axisymmetric perturbations. Two sets of neutral modes are discovered. The first set corresponds to marginally unstable…
We study extremal properties of spherical random polytopes, the convex hull of random points chosen from the unit Euclidean sphere in $\mathbb{R}^n$. The extremal properties of interest are the expected values of the maximum and minimum…
We investigate symmetry-breaking phenomena in semilinear elliptic systems on the unit ball in $\mathbb{R}^3$, focusing on the emergence of non-radial solution branches with prescribed spatial and internal symmetries. Extending previous…
We study radial symmetry of large solutions of the semi-linear elliptic problem \Delta u + \nabla h.\nabla u = f(|x|,u), and we provide sharp conditions under which the problem has a radial solution. The result is independent of the rate of…