Results 1 to 10 of about 213 (45)
Stable solutions of symmetric systems involving hypoelliptic operators [PDF]
Journal of Functional Analysis, 2017 Let X and Y be two noncommuting vector fields in an open set Ω in a manifold M equipped with a sub-Riemannian structure. We examine stable solutions of the following symmetric system ∆XY ui = Hi(u1, · · · , um) in Ω for 1 ≤ i ≤ m, when the operator ∆XY ...
Mostafa Fazly
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Tug-of-war with Kolmogorov [PDF]
Journal of Differential Equations, 2022 We introduce a new class of strongly degenerate nonlinear parabolic PDEs ((p − 2)∆ ∞,X + ∆X )u(X,Y, t) + (m + p)(X · ∇Y u(X,Y, t) − ∂tu(X,Y, t)) = 0, (X,Y, t) ∈ R × R × R, p ∈ (1,∞), combining the classical PDE of Kolmogorov and the normalized p-Laplace ...
Carmina Fjellstrom +2 more
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On the fine properties of parabolic measures associated to strongly degenerate parabolic operators of Kolmogorov type [PDF]
Advances in Mathematics, 2020 We consider strongly degenerate parabolic operators of the form L := ∇X · (A(X,Y, t)∇X) +X · ∇Y − ∂t in unbounded domains Ω = {(X,Y, t) = (x, xm, y, ym, t) ∈ R m−1 × R× R × R× R | xm > ψ(x, y, t)}.
M. Litsgaard, K. Nystrom
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Journal of Mathematical Inequalities, 2022 Let G = ( RN ,◦,δλ ) be a homogeneous group, Q be the homogeneous dimension of G , X0,X1, . . . ,Xm be left invariant real vector fields on G and satisfy Hörmander’s rank condition on RN . Assume that X1, . . . ,Xm (m N − 1) are homogeneous of degree one
V. Guliyev
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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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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 +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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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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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 +4 more
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