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A Liouville theorem for elliptic equations with a potential on infinite graphs [PDF]
Calculus of Variations and Partial Differential Equations, 2023 We investigate the validity of the Liouville property for a class of elliptic equations with a potential, posed on infinite graphs. Under suitable assumptions on the graph and on the potential, we prove that the unique bounded solution is u≡0 ...
Stefano Biagi, Giulia Meglioli, F. Punzo
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A Liouville theorem in the Heisenberg group [PDF]
Journal of the European Mathematical Society (Print), 2023 In this paper, we classify positive solutions to the critical semilinear elliptic equation in the Heisenberg group \mathbb{H}^{1} . We prove that they are the Jerison–Lee’s bubbles.
G. Catino +3 more
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Quantum Liouville theorem based on Haar measure [PDF]
Physical review B, 2023 Liouville theorem (LT) reveals robust incompressibility of distribution function in phase space, given arbitrary potentials. However, its quantum generalization, Wigner flow, is compressible, i.e., LT is only conditionally true (e.g., for perfect ...
B. Song, J.D.H. Smith, L. Luo, J. Wang
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Liouville theorem on Ricci shrinkers with constant scalar curvature and its application [PDF]
Journal für die Reine und Angewandte Mathematik, 2022 In this paper we consider harmonic functions on gradient shrinking Ricci solitons with constant scalar curvature. A Liouville theorem is proved without using gradient estimate: any bounded harmonic function is constant on gradient shrinking Ricci ...
Weixiong Mai, Jianyu Ou
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Liouville theorem and a priori estimates of radial solutions for a non-cooperative elliptic system [PDF]
Nonlinear Analysis, 2021 Liouville theorems for scaling invariant nonlinear elliptic systems (saying that the system does not possess nontrivial entire solutions) guarantee a priori estimates of solutions of related, more general systems.
P. Quittner
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The Borg’s Theorem for Singular Sturm-Liouville Problem with Non-Separated Boundary Conditions [PDF]
Mathematics Interdisciplinary Research, 2023 In this paper, we consider a Sturm-Liouville equation with non-separated boundary conditions on a finite interval. We discuss some properties of solutions of the Sturm-Liouville equation, where the potential function has a singularity in the ...
Maedeh Bagherzadeh, Abdolali Neamaty
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Maximum principles, Liouville theorem and symmetry results for the fractional $g-$Laplacian [PDF]
, 2021 We study different maximum principles for non-local non-linear operators with non-standard growth that arise naturally in the context of fractional Orlicz-Sobolev spaces and whose most notable representative is the fractional $g-$Laplacian: \[ (-\Delta_g)
Sandra M. Molina, A. Salort, H. Vivas
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A Liouville theorem for a class semilinear elliptic equations on the Heisenberg group [PDF]
Advances in Mathematics, 2020 We obtain an entire Liouville type theorem to the classical semilinear subcritical elliptic equation on Heisenberg group. A pointwise estimate near the isolated singularity was also proved.
Xinan Ma, Q. Ou
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Applied Mathematics and Computation, 2021 We first verify the global well-posedness of the impulsive reaction-diffusion equations on infinite lattices. Then we establish that the generated process by the solution operators has a pullback attractor and a family of Borel invariant probability ...
Caidi Zhao, Huite Jiang, T. Caraballo
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A Liouville theorem for Lévy generators [PDF]
Positivity (Dordrecht), 2020 Under mild assumptions, we establish a Liouville theorem for the “Laplace” equation Au=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs ...
F. Kühn
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