Results 31 to 40 of about 7,152,101 (256)
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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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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A Liouville type theorem for ancient Lagrangian mean curvature flows [PDF]
Communications in Partial Differential Equations. We prove a Liouville type result for convex solutions of the Lagrangian mean curvature flow with restricted quadratic growth assumptions at antiquity on the solutions.
Arunima Bhattacharya +2 more
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A Liouville-Type Theorem for the Lane–Emden Equation in a Half-space [PDF]
International mathematics research notices, 2020 We prove that the Dirichlet problem for the Lane–Emden equation in a half-space has no positive solution that is monotone in the normal direction. As a consequence, this problem does not admit any positive classical solution that is bounded on finite ...
L. Dupaigne, B. Sirakov, P. Souplet
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A Liouville-type theorem in a half-space and its applications to the gradient blow-up behavior for superquadratic diffusive Hamilton–Jacobi equations [PDF]
Communications in Partial Differential Equations, 2019 We consider the elliptic and parabolic superquadratic diffusive Hamilton–Jacobi equations: and with p > 2 and homogeneous Dirichlet conditions. For the elliptic problem in a half-space, we prove a Liouville-type classification, or symmetry result, which ...
Roberta Filippucci, P. Pucci, P. Souplet
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A Liouville-type Theorem for Schrödinger Operators [PDF]
Communications in Mathematical Physics, 2007 14 pages, the main result was improved, and a few more applications were ...
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A Liouville-Type Theorem for Elliptic Systems [PDF]
, 1994 The authors consider the system \(- \triangle u = v^ \alpha\), \(- \triangle v = u^ \beta\) in the whole of \(\mathbb{R}^ N\), \(N \geq 3\). The question is to determine for which values of the exponents \(\alpha\) and \(\beta\) the only nonnegative solution \((u,v)\) is the trivial one.
de Figueiredo, D. G., Felmer, P. L.
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A Liouville type theorem for the Schrödinger operator [PDF]
Proceedings of the American Mathematical Society, 1999 In this paper we prove that the equation Δ u (
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Liouville theorems for Hénon type Choquard Equation
Communications on Pure and Applied Analysis, 2023 In this paper, the authors study an equation of Choquard type in \(\mathbb{R} ^{N}\): \[ -\Delta u=\left\vert x\right\vert ^{\alpha}\left\vert u\right\vert ^{p-2} u\int_{\mathbb{R}^{N}}\frac{\left\vert y\right\vert ^{\alpha}\left\vert u(y)\right\vert ^{p}}{\left\vert x-y\right\vert ^{N-\mu}}dy, \] where ...
Dong, Jing, He, Haiyang
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