Results 71 to 80 of about 641,065 (281)
A Lot of “Counterexamples” to Liouville's Theorem
Journal of Mathematical Analysis and Applications, 1996 We prove in this paper that, given α ∈ (0, 1/2), there exists a linear manifold M of entire functions satisfying that M is dense in the space of all entire functions and, in addition, limz→∞ exp(|z|α) f(j)(z) = 0 on any plane strip for every f ∈ M and for every derivation index j.
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Liouville's theorem in conformal geometry
Journal de Mathématiques Pures et Appliquées, 2007 AbstractLiouville's theorem states that all conformal transformations of En and Sn (n⩾3) are restrictions of Möbius transformations. As a generalization, we determine all conformal mappings of semi-Riemannian manifolds preserving pointwise the Ricci tensor.
Wolfgang Kühnel, Hans-Bert Rademacher
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A sharp Liouville theorem for elliptic operators [PDF]
Rendiconti Lincei, Matematica e Applicazioni, 2010 We introduce a new condition on elliptic operators L = \frac 1 2 Δ + b\cdot ∇ which ensures the validity of the Liouville property, i.e., all smooth bounded solutions to Lu = 0 on ℝ^d
PRIOLA, Enrico, F. Y. Wang
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Non-Existence Results for Stable Solutions to Weighted Elliptic Systems including Advection Terms
Mathematics, 2022 In this paper, we study a non-linear weighted Grushin system including advection terms. We prove some Liouville-type theorems for stable solutions of the system, based on the comparison property and the bootstrap iteration.
Suleman Alfalqi
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The Liouville theorems for elliptic equations with nonstandard growth [PDF]
, 2014 We study solutions and supersolutions of homogeneous and nonhomogeneous $\mathcal{A}$-harmonic equations with nonstandard growth in $\mathbb{R}^n$. Various Liouville-type theorems and nonexistence results are proved.
Tomasz Adamowicz, P. G'orka
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Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6425-6446, April 2025.ABSTRACT The well‐posedness results for mild solutions to the fractional neutral stochastic differential system with Rosenblatt process with Hurst index Ĥ∈12,1$$ \hat{H}\in \left(\frac{1}{2},1\right) $$ is discussed in this article. To demonstrate the results, the concept of bounded integral contractors is combined with the stochastic result and ...
Dimplekumar N. Chalishajar +3 more
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A proof of Liouville’s theorem [PDF]
Proceedings of the American Mathematical Society, 1961 1. S. Bochner, Group invariance of Cauchy's formula in several variables, Ann. of Math. vol. 45 (1944) pp. 686-707. 2. E. Heinz, Ein v. Neumannscher Satz iuber beschriinkte Operatoren im Hilbertschen Raum, Nachr. Akad. Wiss. Gottingen. Math.-Phys. Kl. Ila. (1952) pp. 5-6. 3. J.
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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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On Hybrid Type Nonlinear Fractional Integrodifferential Equations
Mathematics, 2020 In this paper, we introduce and investigate a hybrid type of nonlinear Riemann Liouville fractional integro-differential equations. We develop and extend previous work on such non-fractional equations, using operator theoretical techniques, and find the ...
Faten H. Damag +2 more
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Liouville theorems for the polyharmonic Henon-Lane-Emden system [PDF]
, 2013 We study Liouville theorems for the following polyharmonic H\'{e}non-Lane-Emden system \begin{eqnarray*} \left\{\begin{array}{lcl} (-\Delta)^m u&=& |x|^{a}v^p \ \ \text{in}\ \ \mathbb{R}^n,\\ (-\Delta)^m v&=& |x|^{b}u^q \ \ \text{in}\ \ \mathbb{R}^n ...
Mostafa Fazly
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