Results 41 to 50 of about 646,050 (293)
Liouville theorems and classification results for a nonlocal Schrödinger equation
, 2018 In this paper, we study the existence and the nonexistence of positive classical solutions of the static Hartree-Poisson equation \begin{document}$-Δ u = pu^{p-1}(|x|^{2-n}*u^p),\;\; u>0 \;\;in\;\; R^n, $ \end{document} where \begin{document}$n ≥ 3$\end ...
Y. Lei
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On the Liouville Theorem for Harmonic Maps [PDF]
Proceedings of the American Mathematical Society, 1982 Suppose M M and N N are complete Riemannian manifolds; M M with Ricci curvature bounded below by − A - A , A ⩾ 0 A \geqslant 0 , N N with sectional curvature bounded above by a positive constant K
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${L^p}$-Liouville Theorems for Invariant Partial Differential Operators in ${\mathbb{R}^n}$
, 2014 We prove some $L^p$-Liouville theorems for hypoelliptic second order Partial Differential Operators left translation invariant with respect to a Lie group composition law in $\mathbb{R}^n$.
Kogoj, Alessia E., Lanconelli, Ermanno
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Journal of Function Spaces, 2021 The existence of three solutions for nonlinear operator equations is established via index theory for linear self-adjoint operator equations, critical point reduction method, and three critical points theorems obtained by Brezis-Nirenberg, Ricceri, and ...
Mingliang Song, Shuyuan Mei
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Liouville Theorems for a General Class of Nonlocal Operators [PDF]
, 2015 In this paper, we study the equation ℒu=0$\mathcal {L} u=0$ in ℝN$\mathbb {R}^{N}$, where ℒ$\mathcal {L}$ belongs to a general class of nonlocal linear operators which may be anisotropic and nonsymmetric.
M. Fall, T. Weth
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A form of classical Liouville theorem
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1997 Let \(u\) be a harmonic function on \(\mathbb{R}^d\) \((d\geq 2)\) and let \(M(r)\) denote the maximum value of \(u^+\) over the sphere of centre 0 and radius \(r\). It is a classical result that, if \(r^{-n-1} M(\tau)\to 0\) as \(r\to\infty\) for some non-negative integer \(n\), then \(u\) is a polynomial of degree at most \(n\) [see the Appendix in ...
Nakai, Mitsuru, Tada, Toshimasa
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Weighted ${L^p}$-Liouville Theorems for Hypoelliptic Partial Differential Operators on Lie Groups
, 2015 We prove weighted $L^p$-Liouville theorems for a class of second order hypoelliptic partial differential operators $\mathcal{L}$ on Lie groups $\mathbb{G}$ whose underlying manifold is $n$-dimensional space.
Bonfiglioli, Andrea, Kogoj, Alessia E.
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Some Liouville Theorems on Finsler Manifolds
Mathematics, 2019 We give some Liouville type theorems of L p harmonic (resp. subharmonic, superharmonic) functions on a complete noncompact Finsler manifold.
Minqiu Wang, Songting Yin
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The Partial Inverse Spectral and Nodal Problems for Sturm–Liouville Operators on a Star-Shaped Graph
Mathematics, 2022 We firstly prove the Horváth-type theorem for Sturm–Liouville operators on a star-shaped graph and then solve a new partial inverse nodal problem for this operator.
Xian-Biao Wei +2 more
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Extensions of Liouville theorems
Journal of Mathematical Analysis and Applications, 1982 AbstractThe method of deriving Liouville's theorem for subharmonic functions in the plane from the corresponding Hadamard three-circles theorem is extended to a more general and abstract setting. Two extensions of Liouville's theorem for vector-valued holomorphic functions of several complex variables are also mentioned.
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