Results 11 to 20 of about 7,045,461 (221)
A Liouville-Type Theorem for Harmonic Functions on Exterior Domains [PDF]
Journal of Mathematical Analysis and Applications, 2000 Liouville's classical theorem that a function harmonic in \(\mathbb{R}^2\) that is bounded below is a constant does not extend to \(\mathbb{R}^2\) punctured at the origin. Via some interesting preliminaries on convex sets in \(\mathbb{R}^2\), the authors prove that if \(K\) is a non-empty compact convex set in \(\mathbb{R}^2\) and \(f\) is a real ...
CAMMAROTO, Filippo, CHINNI', Antonia
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A Liouville-type Theorem on half-spaces for sub-Laplacians [PDF]
Proceedings of the American Mathematical Society, 2014 Summary: Let \( \mathcal {L}\) be a sub-Laplacian on \( \mathcal {L}^N\) and let \( \mathbb{G}=(\mathcal {L}^N,\circ ,\delta _\lambda )\) be its related homogeneous Lie group. Let \( \mathbb{E}\) be a Euclidean subgroup of \( \mathcal {L}^N\) such that the orthonormal projection \( \pi :\mathbb{G} \longrightarrow \mathbb{E}\) is a homomorphism of ...
Alessia E. Kogoj, Alessia E. Kogoj
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An improved Liouville type theorem for Beltrami flows [PDF]
, 2022 In this note, we improved the Liouville type theorem for the Beltrami flows. Two different methods are used to prove it. One is the monotonicity method, and the other is proof by contradiction.
Zhang, Zhibing, Wang, Na
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A Liouville theorem for a class of reaction–diffusion systems with fractional diffusion
, 2023 We prove a Liouville theorem on the positive bounded entire solution of a class of reaction–diffusion systems with fractional diffusion.
Guo, Jong-Shenq;Shimojo, Masahiko
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Cut loci and conjugate loci on Liouville surfaces [PDF]
, 2011 In the earlier paper (Itoh and Kiyohara, Manuscr Math 114:247–264, 2004), we showed that the cut locus of a general point on two-dimensional ellipsoid is a segment of a curvature line and proved "Jacobi’s last geometric statement" on the singularities of
Jin-ichi Itoh +3 more
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Remarks on a Liouville-Type Theorem for Beltrami Flows [PDF]
International Mathematics Research Notices, 2014 We present a simple, short and elementary proof that if $v$ is a Beltrami flow with a finite energy in $\mathbb R^3$ then $v=0$. In the case of the Beltrami flows satisfying $v\in L^\infty _{loc} (\Bbb R^3) \cap L^q(\Bbb R^3)$ with $q\in [2, 3)$, or $|v(x)|=O(1/|x|^{1+\varepsilon})$ for some $\varepsilon >0$, we provide a different, simple proof ...
Chae, Dongho, Constantin, Peter
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Wintner-type nonoscillation theorems for conformable linear Sturm-Liouville differential equations [PDF]
Opuscula MathematicaIn this study, we addressed the nonoscillation of th Sturm-Liouville differential equation with a differential operator, which corresponds to a proportional-derivative controller. The equation is a conformable linear differential equation. A Wintner-type
Kazuki Ishibashi
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Advances in Difference Equations, 2021 This paper is concerned with the existence and uniqueness of solutions for a coupled system of Liouville–Caputo type fractional integro-differential equations with multi-point and sub-strip boundary conditions.
Ahmed Alsaedi +3 more
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A new kind of uniqueness theorems for inverse Sturm-Liouville problems
Boundary Value Problems, 2017 We prove Marchenko-type uniqueness theorems for inverse Sturm-Liouville problems. Moreover, we prove a generalization of Ambarzumyan’s theorem.
Yuri Ashrafyan
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Современная математика: Фундаментальные направления, 2023 Using the fixed point theorem in partially ordered sets, we obtain sufficient conditions for the existence of a unique positive solution to a boundary-value problem of the Sturm-Liouville type for a nonlinear ordinary differential equation, and give an ...
G. E. Abduragimov +2 more
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