Results 1 to 10 of about 203 (41)

Liouville theorems for Kirchhoff-type parabolic equations and system on the Heisenberg group

Open Mathematics, 2023
In this article, the Liouville theorems for the Kirchhoff-type parabolic equations on the Heisenberg group were established. The main technique for proving the result relies on the method of test functions.
Shi Wei
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Multiplicity of solutions for a class of critical Schrödinger-Poisson systems on the Heisenberg group

Open Mathematics, 2023
We deal with multiplicity of solutions to the following Schrödinger-Poisson-type system in this article: ΔHu−μ1ϕ1u=∣u∣2u+Fu(ξ,u,v),inΩ,−ΔHv+μ2ϕ2v=∣v∣2v+Fv(ξ,u,v),inΩ,−ΔHϕ1=u2,−ΔHϕ2=v2,inΩ,ϕ1=ϕ2=u=v=0,on∂Ω,\left\{\begin{array}{ll}{\Delta }_{H}u-{\mu }_{1}{
Li Shiqi, Song Yueqiang
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One-dimensional inverse problems of determining the kernel of the integro-differential heat equation in a bounded domain

Nonautonomous Dynamical Systems, 2023
The integro-differential equation of heat conduction with the time-convolution integral on the right side is considered. The direct problem is the initial-boundary problem for this integro-differential equation.
Durdiev Durdimurod Kalandarovich, Jumaev Jonibek Jamolovich   +1 more
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Existence of nontrivial solutions for critical Kirchhoff-Poisson systems in the Heisenberg group

Advanced Nonlinear Studies, 2022
This article is devoted to the study of the combined effects of logarithmic and critical nonlinearities for the Kirchhoff-Poisson system −M∫Ω∣∇Hu∣2dξΔHu+μϕu=λ∣u∣q−2uln∣u∣2+∣u∣2uinΩ,−ΔHϕ=u2inΩ,u=ϕ=0on∂Ω,\left\{\begin{array}{ll}-M\left(\mathop ...
Pucci Patrizia, Ye Yiwei
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On the critical Choquard-Kirchhoff problem on the Heisenberg group

Advances in Nonlinear Analysis, 2022
In this paper, we deal with the following critical Choquard-Kirchhoff problem on the Heisenberg group of the form: M(‖u‖2)(−ΔHu+V(ξ)u)=∫HN∣u(η)∣Qλ∗∣η−1ξ∣λdη∣u∣Qλ∗−2u+μf(ξ,u),M\left(\Vert u{\Vert }^{2})\left(-{\Delta }_{{\mathbb{H}}}u\left+V\left(\xi )u)=\
Sun Xueqi, Song Yueqiang, Liang Sihua
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Critical nonlocal Schrödinger-Poisson system on the Heisenberg group

Advances in Nonlinear Analysis, 2021
In this paper, we are concerned with the following a new critical nonlocal Schrödinger-Poisson system on the Heisenberg group:
Liu Zeyi, Tao Lulu, Zhang Deli, Liang Sihua, Song Yueqiang   +4 more
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On the existence of nonnegative radial solutions for Dirichlet exterior problems on the Heisenberg group

Demonstratio Mathematica, 2023
We investigate the existence and nonexistence of nonnegative radial solutions to exterior problems of the form ΔHmu(q)+λψ(q)K(r(q))f(r2−Q(q),u(q))=0{\Delta }_{{{\mathbb{H}}}^{m}}u\left(q)+\lambda \psi \left(q)K\left(r\left(q))f\left({r}^{2-Q}\left(q),u ...
Jleli Mohamed
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Asymptotically Mean Value Harmonic Functions in Doubling Metric Measure Spaces

Analysis and Geometry in Metric Spaces, 2022
We consider functions with an asymptotic mean value property, known to characterize harmonicity in Riemannian manifolds and in doubling metric measure spaces.
Adamowicz Tomasz, Kijowski Antoni, Soultanis Elefterios   +2 more
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Supplement a high-dimensional time fractional diffusion equation

Alexandria Engineering Journal, 2023
In this article, we discussed a high-dimensional time fractional diffusion equation which is used to write many nonlinear phenomena in three dimensional space diffusion processes.
Jian-Gen Liu, Fa-Zhan Geng, Xin Li
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(p,Q) systems with critical singular exponential nonlinearities in the Heisenberg group

Open Mathematics, 2020
The paper deals with the existence of solutions for (p,Q)(p,Q) coupled elliptic systems in the Heisenberg group, with critical exponential growth at infinity and singular behavior at the origin.
Pucci Patrizia, Temperini Letizia
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