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pro vyhledávání: '"45g15"'
A system of singular integral equations with monotone and concave nonlinearity in the subcritical case is investigated. The specified system and its scalar analog have direct applications in various areas of physics and biology. In particular, scalar
Externí odkaz:
http://arxiv.org/abs/2410.19423
We introduce an efficient discretization of a novel fractional-order adaptive exponential (FrAdEx) integrate-and-fire model, which is used to study the fractional-order dynamics of neuronal activities. The discretization is based on extension of L1-t
Externí odkaz:
http://arxiv.org/abs/2404.13554
Autor:
da Silva, Genival
The existence of radially symmetric solutions is discussed for a Lane-Emden type system. This answer a question posed by da Silva and do O (2024). We also comment on the inhomogeneous version of the same system and discuss some open questions.
Externí odkaz:
http://arxiv.org/abs/2403.14030
Autor:
Jaramillo, Gabriela
We prove existence of spiral waves in oscillatory media with nonlocal coupling. Our starting point is a nonlocal complex Ginzburg-Landau (cGL) equation, rigorously derived as an amplitude equation for integro-differential equations undergoing a Hopf
Externí odkaz:
http://arxiv.org/abs/2401.15226
This paper focuses on the modeling of experiments conducted by Billock and Tsou [V. A. Billock and B. H. Tsou, Proc. Natl. Acad. Sci. USA, 104 (2007), pp. 8490--8495] using an Amari-type neural field that models the average membrane potential of neur
Externí odkaz:
http://arxiv.org/abs/2401.09108
In this paper, we obtain the reversed Hardy-Littlewood-Sobolev inequality with vertical weights on the upper half space and discuss the extremal functions. We show that the sharp constants in this inequality are attained by introducing a renormalizat
Externí odkaz:
http://arxiv.org/abs/2311.03933
Autor:
Guseynov, Yevgeniy
We define a deterministic integral with respect to irregular paths as a limit of standard line integrals and completely describe a class of all paths for which this integral exists for functions with H\"older exponent in the range of (0,1]. With the
Externí odkaz:
http://arxiv.org/abs/2309.06316
Publikováno v:
Open Mathematics, Vol 22, Iss 1, Pp 565-606 (2024)
In this article, we study the following weighted integral system: u(x)=∫R+n+1yn+1βf(u(y),v(y))∣x−y∣λdy,x∈R+n+1,v(x)=∫R+n+1yn+1βg(u(y),v(y))∣x−y∣λdy,x∈R+n+1.\left\{\begin{array}{l}u\left(x)=\mathop{\displaystyle \int }\limits_{
Externí odkaz:
https://doaj.org/article/496b584cd3af4395acdfb0af35a1e2fb
Autor:
Dou, Jingbo, Ma, Jingjing
In this paper, we establish a class of Hardy-Littlewood-Sobolev inequality with partial variable weight functions on the upper half space using a weighted Hardy type inequality. Overcoming the impact of weighted functions, the existence of extremal f
Externí odkaz:
http://arxiv.org/abs/2308.06976
We provide new results regarding the localization of the solutions of nonlinear operator systems. We make use of a combination of Krasnosel'ski\u{\i} cone compression-expansion type methodologies and Schauder-type ones. In particular we establish a l
Externí odkaz:
http://arxiv.org/abs/2307.06053