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pro vyhledávání: '"47j05"'
In this paper, we study the $T$-periodic solutions of the parameter-dependent $\phi$-Laplacian equation \begin{equation*} (\phi(x'))'=F(\lambda,t,x,x'). \end{equation*} Based on the topological degree theory, we present some atypical bifurcation resu
Externí odkaz:
http://arxiv.org/abs/2406.00325
In this paper we propose an approach for solving systems of nonlinear equations without computing function derivatives. Motivated by the application area of tomographic absorption spectroscopy, which is a highly-nonlinear problem with variables coupl
Externí odkaz:
http://arxiv.org/abs/2405.08635
In this paper we deal with an equation in nonlinear combination of iterates. Although it can be reduced by the logarithm conjugacy to a form for application of Schauder's or Banach's fixed point theorems, a difficulty called Zero Problem is encounter
Externí odkaz:
http://arxiv.org/abs/2401.06420
Autor:
Fechner, Włodzimierz, Gselmann, Eszter
The paper aims to provide a full characterization of all operators $T\colon \mathscr{P}(\mathbb{C}) \to \mathscr{P}(\mathbb{C})$ acting on the space of all complex polynomials that satisfy the Leibniz rule \[ T(f\cdot g)= T(f)\cdot g+f\cdot T(g) \] f
Externí odkaz:
http://arxiv.org/abs/2311.04671
In this work we prove uniqueness of distributional solutions to $2D$ Navier-Stokes equations in vorticity form $u_t-\nu\Delta u+ div (K(u)u)=0$ on $(0,\infty)\times\mathbb{R}^2$ with Radon measures as initial data, where $K$ is the Biot-Savart operat
Externí odkaz:
http://arxiv.org/abs/2309.13910
Let $r$ be a positive integer, $N$ be a nonnegative integer and $\Omega \subset \mathbb{R}^{r}$ be a domain. Further, for all multi-indices $\alpha \in \mathbb{N}^{r}$, $|\alpha|\leq N$, let us consider the partial differential operator $D^{\alpha}$
Externí odkaz:
http://arxiv.org/abs/2309.03572
This work is concerned with the existence of mild solutions and the uniqueness of distributional solutions to nonlinear Fokker-Planck equations with nonlocal operators $\Psi(-\Delta)$, where $\Psi$ is a Bernstein function. As applications, the existe
Externí odkaz:
http://arxiv.org/abs/2308.06388
Autor:
Cibulka, Radek
Ioffe's criterion and various reformulations of it have become a~standard tool in proving theorems guaranteeing various regularity properties such as metric regularity, i.e., the openness with a linear rate around the reference point, of a~(set-value
Externí odkaz:
http://arxiv.org/abs/2307.07274
{Let $N, k$ be positive integers with $k\geq 2$, and $\Omega \subset \mathbb{R}^{N}$ be a domain.} By the well-known properties of the Laplacian and the gradient, we have \[ \Delta(f\cdot g)(x)=g(x) \Delta f(x)+f(x) \Delta g(x)+2\langle \nabla f(x),
Externí odkaz:
http://arxiv.org/abs/2306.02788
Autor:
Zubelevich, Oleg
We show that for the case of uniformly convex Banach spaces the conditions of the Brondsted fixed point theorem can be relaxed.
Externí odkaz:
http://arxiv.org/abs/2302.07846