Zobrazeno 1 - 10
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pro vyhledávání: '"fractional Laplacian"'
Autor:
Tian Junshan, Zhang Binlin
Publikováno v:
Advances in Nonlinear Analysis, Vol 13, Iss 1, Pp 349-381 (2024)
In this article, we study the following fractional Kirchhoff-type problems with critical and sublinear nonlinearities: a+b∬RN×RN∣u(x)−u(y)∣2∣x−y∣N+2sdxdy(−Δ)su=λuq−1+u2s*−1,u>0,inΩ,u=0,inRN\Ω,∫RNu2dx=c2,\left\{\begin{array}
Externí odkaz:
https://doaj.org/article/e843a0dac58a48e4b98b007c7df88671
Autor:
Gu Caihong, Tang Yanbin
Publikováno v:
Advances in Nonlinear Analysis, Vol 13, Iss 1, Pp 385-399 (2024)
In this article, we consider the global and local well-posedness of the mild solutions to the Cauchy problem of fractional drift diffusion system with higher-order nonlinearity. The main difficulty comes from the higher-order nonlinearity. Instead of
Externí odkaz:
https://doaj.org/article/c4e8e61ae3d34d6bb148c34230df6137
Publikováno v:
Bulletin of Mathematical Sciences, Vol 14, Iss 02 (2024)
The aim of this paper is to discuss the existence of normalized solutions to the following nonlocal double phase problems driving by the discrete fractional Laplacian: ( − Δ𝔻)pαu(k) + μ(−Δ 𝔻)qβu(k) + ω(k)|u(k)|p−2u(k) = λ|u(k)|q−
Externí odkaz:
https://doaj.org/article/324306c2e2e7425f9e1933b23d2fa917
Publikováno v:
Advanced Nonlinear Studies, Vol 24, Iss 2, Pp 399-414 (2024)
In this paper, let α be any real number between 0 and 2, we study the following semi-linear elliptic system involving the fractional Laplacian: (−Δ)α/2u(x)=f(u(x),v(x)),x∈Rn,(−Δ)α/2v(x)=g(u(x),v(x)),x∈Rn. $\begin{cases}{\left(-{\Delta}\r
Externí odkaz:
https://doaj.org/article/6d08845db2504dc0b1bd491915d90a40
Publikováno v:
Advanced Nonlinear Studies, Vol 24, Iss 2, Pp 303-334 (2024)
In this paper we study the following nonlinear fractional Hartree (or Choquard-Pekar) equation (−Δ)su+μu=(Iα*F(u))F′(u) inRN, ${\left(-{\Delta}\right)}^{s}u+\mu u=\left({I}_{\alpha }{\ast}F\left(u\right)\right){F}^{\prime }\left(u\right)\quad
Externí odkaz:
https://doaj.org/article/45c1dc70ce1b4a2b9fad14a6bea3f000
Publikováno v:
Advanced Nonlinear Studies, Vol 24, Iss 2, Pp 359-398 (2024)
In this paper, we summarize some of the recent developments in the area of fractional elliptic and parabolic equations with focus on how to apply the sliding method and the method of moving planes to obtain qualitative properties of solutions. We wil
Externí odkaz:
https://doaj.org/article/41b8af497d6b4ad4b0a8ca51fdf86e70
Autor:
Li Yan
Publikováno v:
Advanced Nonlinear Studies, Vol 24, Iss 2, Pp 451-462 (2024)
We investigate the Dirichelt problem involving the fractional Laplacian in the upper half-space R+n=x∈Rn∣x1>0 ${\mathbb{R}}_{+}^{n}=\left\{x\in {\mathbb{R}}^{n}\mid {x}_{1}{ >}0\right\}$ : (−Δ)su(x)=f(u(x)),x∈R+n, u(x)>0,x∈R+n, u(x)=0,x∉
Externí odkaz:
https://doaj.org/article/9dc5ce9ca25648daa254c53a06ef298f
Autor:
Ruonan Liu, Tomás Caraballo
Publikováno v:
AIMS Mathematics, Vol 9, Iss 4, Pp 8020-8042 (2024)
In this paper, the asymptotic behavior of solutions to a fractional stochastic nonlocal reaction-diffusion equation with polynomial drift terms of arbitrary order in an unbounded domain was analysed. First, the stochastic equation was transformed int
Externí odkaz:
https://doaj.org/article/10cb269b0ed84b65a4eeaf580fc4f554
Akademický článek
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Publikováno v:
Boundary Value Problems, Vol 2024, Iss 1, Pp 1-13 (2024)
Abstract In this paper, we are concerned with the Kirchhoff-type variable-order fractional Laplacian problems involving critical exponents and logarithmic nonlinearity. By using the constraint variational method, we show the existence of one least en
Externí odkaz:
https://doaj.org/article/894e0c9b71ca47c993946830116350da