On the nonrigidity of trace modules
Lindo. Source: Journal of Commutative Algebra, Forthcoming articles, --....
Mathematics - Research News
Infinitely many solutions for a class of superlinear problems involving variable exponents
Bin Ge, Li-Yan Wang. Source: Advances in Differential Equations, Volume 25, Number 3/4, 191--212.Abstract: We are concerned with the following $p(x)$-Laplacian equations in $\mathbb{R}^N$ $$ -\triangle_{p(x)} u+V(x)|u|^{p(x)-2}u= f(x,u)\ \ {\rm in }\; \mathbb{R}^N. $$ Based on a direct sum...
Bifurcation of positive radial solutions for a prescribed mean curvature problem on an exterior domain
Rui Yang, Yong-Hoon Lee. Source: Advances in Differential Equations, Volume 25, Number 3/4, 161--190.Abstract: In this paper, we study the existence of positive radial solutions for a prescribed mean curvature problem on an exterior domain. Based on $C^1$-regularity of solutions, which is closely...
Solutions to upper critical fractional Choquard equations with potential
Xinfu Li, Shiwang Ma, Guang Zhang. Source: Advances in Differential Equations, Volume 25, Number 3/4, 135--160.Abstract: In this paper, the upper critical fractional Choquard equation is considered. The interest in studying such equation comes from its strong connections with mathematical physics,...
On ground state of fractional spinor Bose Einstein condensates
Daomin Cao, Jinchun He, Haoyuan Xu, Meihua Yang. Source: Advances in Differential Equations, Volume 25, Number 3/4, 105--134.Abstract: In this paper, we prove the existence of the positive ground state solution to fractional spin-1 Bose-Einstein condensation(BEC) in one dimension. ...
Dissipative reaction diffusion systems with polynomial growth
Takashi Suzuki. Source: Advances in Differential Equations, Volume 25, Number 1/2, 81--104.Abstract: We study quasi-positive dissipative reaction diffusion systems with polynomial growth and show several criteria for global-in-time existence of the classical solution uniformly bounded. ...
Large time asymptotics for the fractional nonlinear Schrödinger equation
Nakao Hayashi, Pavel I. Naumkin. Source: Advances in Differential Equations, Volume 25, Number 1/2, 31--80.Abstract: We consider the Cauchy problem for the fractional nonlinear Schrödinger equation \[ \left\{ \begin{array} [c]{c}% i\partial_{t}u+\frac{1}{\alpha} \left| \partial_{x} \right|...
Symmetric Lyapunov center theorem for orbit with nontrivial isotropy group
Marta Kowalczyk, Ernesto Pérez-Chavela, Sławomir Rybicki. Source: Advances in Differential Equations, Volume 25, Number 1/2, 1--30.Abstract: In this article, we prove two versions of the Lyapunov center theorem for symmetric potentials. We consider a second order autonomous system $$ \ddot...
Cracking Open Black Boxes
Algorithms can be very useful, but lately, with so much data being created and shared, and with the increase in their use in critical areas such as hiring, credit, and health care, algorithms are under intense scrutiny about their fairness. People experience the effects of an algorithm's conclusion,...
Modified $\alpha $ -Bernstein operators with better approximation properties
Arun Kajla, Tuncer Acar. Source: Annals of Functional Analysis, Volume 10, Number 4, 570--582.Abstract: In the present note, following a new approach recently described by Khosravian-Arab, Dehghan, and Eslahchi, we construct a new kind of $\alpha $ -Bernstein operator and study a uniform...