We investigate the existence of nodal (sign-changing) solutions to the Dirichlet problem for a two-parametric family of partially homogeneous (p, q)-Laplace equations −Δpu − Δqu = α|u|p−2u + β|u|q−2u where p ≠ q. By virtue of the Nehari manifolds, the linking theorem, and descendi...

The presented study evaluates the ways in which an extraction or non-extraction orthodontic treatment of distoocclusion in growing patients may affect selected skeletal and dental parameters and anteroposterior dimension of airways in the area of oropharynx as represented in the cephalogram, ...

We consider the Fisher equation for advance of advatageous gene with non-Lipschitzian reaction term. We prove new travelling wave profiles and the convergence of the Cauchy problem to one of those profiles.

The article presents the tasks of a mathematic school leaving examination at Bavarian high schools in May 2017. This tasks are supplemented by brief descriptions of the solutions.

This article is devoted to study the existence of a solution to the periodic nonlinear second order ordinary differential equation with damping u''(x)+ c u'(x)+g(x,u)=f(x) x in [0,T] , u(0)=u(T), u'(0)=u'(T), where c in R, g is a Carath'eodory function, f in L^1(...

We introduce a closure concept for hamiltonicity in the class of {K(1,4),K(1,4)+e}-free graphs, extending the closure for claw-free graphs introduced by Ryjáček (1997). The closure of a {K(1,4),K(1,4)+e}-free graph G with minimum degree at least 6 is uniquely determined, is a line graph...

In this paper, we deal with the discrete Dirichlet operator of the second order and we investigate its Fučík spectrum, which consists of a finite number of algebraic curves. For each non-trivial Fučík curve, we are able to detect a finite number of its points, which ...

Ruled surfaces, i.e., surfaces generated by a one-parametric set of lines, are widely used in the field of applied geometry. An isophote on a surface is a curve consisting of those surface points whose normals form a constant angle with a fixed vector. Choosing the angle&...

Let B1 be a ball in RN centred at the origin and let B0 be a smaller ball compactly contained in B1. For p ∈ (1,∞), using the shape derivative method, we show that the first eigenvalue of the p-Laplacian in annulus B1\B0 strictly decreases as the inner ...

We develop the notion of higher Cheeger constants for a measurable set $\Omega \subset \mathbb{R}^N$. By the $k$-th Cheeger constant we mean the value \[h_k(\Omega) = \inf \max \{h_1(E_1), \dots, h_1(E_k)\},\] where the infimum is taken over all $k$-tu...

We investigate multiplicity and symmetry properties of higher eigenvalues and eigenfunctions of the $p$-Laplacian under homogeneous Dirichlet boundary conditions on certain symmetric domains $\Omega \subset \R^N$. By means of topological arguments, we show how symmetries of $\Omega$ help...

Home team advantage in sports is widely analysed phenomenon. This paper builds on results of recent research that -- instead of points gained -- uses goals scored and conceded to describe home team advantage. Using this approach, the home team advantage is random variable that...

We provide two existence results for sign-changing solutions to the Dirichlet problem for the family of equations $-\Delta_p u -\Delta_q u = \alpha |u|^{p-2}u + \beta |u|^{q-2}u$, where $1<q<p$ and $\alpha$, $\beta$ are parameters. First, we show the existence in&#x...

In this paper we establish the existence of multiple ordered classical solutions for Neumann semilinear elliptic problems and provide qualitative information about them. No symmetry assumptions are required neither on the non-linearity nor on the domain. For some results, the growth of ...

The objective of this paper is to study the stability of the mean-variance portfolio optimization. The results of the mean-variance optimal selection problem are very sensitive to the model parameters (portfolio calibration window and frequency of portfolio rebalancing). There are presented ...

We study in detail the existence, nonexistence and behavior of global minimizers, ground states and corresponding energy levels of the (p,q)-Laplace equation in a bounded domain under zero Dirichlet boundary condition, where p>q>1. A curve on the plane of parameters which allocates...

We find an explicit formula for the coefficients $\alpha_n$, $n \in \mathbb{N}$, of the generalized Maclaurin series for $\sin_p$ provided $p > 2$ is an integer. Our method is based on an expression of the $n$-th derivative of $\sin_p$ in the form \[...

We prove that the two-coloring number of any planar graph is at most 8. This resolves a question of Kierstead et al. (2009). The result is optimal.

We study convergence of the Newton method for solving generalized equations with a continuous but not necessarily smooth single-valued part and a set-valued mapping with closed graph, both acting in Banach spaces. We present a Kantorovich-type theorem concerning r-linear convergence for a&#x...

In this paper we consider a control system coupled with a generalized equation, which we call a differential generalized equation (DGE). This model covers a large territory in control and optimization, such as differential variational inequalities, control systems with constraints, as well&#...