Related papers: Sturm-Picone theorem for fractional nonlocal equat…
We investigate symmetry and quantitative approximate symmetry for an overdetermined problem related to the fractional torsion equation in a regular open, bounded set $\Omega \subseteq \mathbb{R}^n$. Specifically, we show that if…
Levinson's theorem for the Schr\"{o}dinger equation with a cylindrically symmetric potential in two dimensions is re-established by the Sturm-Liouville theorem. The critical case, where the Schr\"{o}dinger equation has a finite zero-energy…
We prove Koebe's conjecture and a version of Schramm's cofat uniformization theorem for domains $\Omega \subset \mathbb C$ satisfying conditions involving quasitripods, i.e., quasisymmetric images of the standard tripod. If the non-point…
We study a nonlocal thermistor problem for fractional derivatives in the conformable sense. Classical Schauder's fixed point theorem is used to derive the existence of a tube solution.
Given any uniform domain $\Omega$, the Triebel-Lizorkin space $F^s_{p,q}(\Omega)$ with $0<s<1$ and $1<p,q<\infty$ can be equipped with a norm in terms of first order differences restricted to pairs of points whose distance is comparable to…
Schmidt's theorem is significantly generalized, to partitions in which periodic but otherwise arbitrary subsets of parts are counted or uncounted. The identification of such sets of partitions with colored partitions satisfying certain…
Consider the quasilinear diffusion problem \[\begin{cases}\mathbf{u}'+\Pi(t,x,\mathbf{u},\Sigma \mathbf{u})\mathbb{A}\mathbf{u}=\mathbf{f}(t,x,\mathbf{u},\Sigma \mathbf{u})&\text{ in }]0,T[\times\Omega,\\\mathbf{u}=\mathbf{0}&\text{ in…
In this work we study a generalized nonlocal thermistor problem with fractional-order Riemann-Liouville derivative. Making use of fixed-point theory, we obtain existence and uniqueness of a positive solution.
In this paper, we formulate a regular $q$-fractional Sturm--Liouville problem (qFSLP) which includes the left-sided Riemann--Liouville and the right-sided Caputo q-fractional derivatives of the same order $\alpha$, $\alpha\in (0,1)$. The…
In this paper we study a Neumann problem for the fractional Laplacian, namely \begin{equation}\left\{ \begin{array}{rcll} \varepsilon^{2s}(- \Delta)^{s}u + u &=& f(u) \ \ &\mbox{in} \ \ \Omega \\ \mathcal{N}_{s}u &=& 0 , \,\, &\text{in}…
In this paper, the tropical Nevanlinna theory is extended for piecewise polynomial continuous functions. By constructing the $n$-th Poisson-Jensen formula, the $n$-th tropical counting, proximity, and characteristic functions are…
Our purpose of this paper is to study the nonexistence of nonnegative very weak solutions of \begin{equation}\label{eq 0.1} \displaystyle (-\Delta)^\alpha u = u^p+\nu\quad {\rm in}\quad \Omega,\qquad\ u=g\quad {\rm in}\quad \mathbb{…
In this paper, we establish Schauder's estimates for the following non-local equations in \mR^d : $$ \partial_tu=\mathscr L^{(\alpha)}_{\kappa,\sigma} u+b\cdot\nabla u+f,\ u(0)=0, $$ where $\alpha\in(1/2,2)$ and $ b:\mathbb R_+\times\mathbb…
Generalized Pauli's theorem, proved by D. S. Shirokov for two sets of anticommuting elements of a real or complexified Clifford algebra of dimension $2^n$, is extended to the case, when both sets of elements depend smoothly on points of…
Motivated by the classification of solutions of harmonic functions, we investigate Liouville type theorems for the fractional Navier-Stokes equations in $\mathbb{R}^3$ under some conditions on the boundedness of fractional derivatives. We…
We begin by proving a local existence result for a fractional Caputo nonlocal thermistor problem. Then, additional existence and continuation theorems are obtained, ensuring global existence of solutions.
For $\alpha\in (1,2)$, we present a generalized central limit theorem for $\alpha$-stable random variables under sublinear expectation. The foundation of our proof is an interior regularity estimate for partial integro-differential…
In this article we are interested on the non-homogeneous fractional Schr\"odinger equation \begin{eqnarray}\label{eq00} &(-\Delta)^{\alpha}u(x) + V(x)u(x) = f(u) + h(x) \mbox{ in } \mathbb{R}^{n}. \end{eqnarray} By using mountain pass…
We show the existence of self-dual semilocal nontopological vortices in a $\Phi^2$ Chern-Simons (C-S) theory. The model of scalar and gauge fields with a $SU(2)_{global} \times U(1)_{local}$ symmetry includes both the C-S term and an…
The mathematical theory of a novel variational approximation scheme for general second and fourth order partial differential equations \begin{equation}\label{eq: A} \partial_t u - \nabla\cdot\Big(u\nabla\frac{\delta\phi}{\delta…