Liouville theorems for stable weak solutions of elliptic problems involving Grushin operator
Communications on Pure and Applied Analysis, 2020 We consider the boundary value problem \begin{document}$\begin{equation*} \begin{cases} -{\rm div}_G(w_1\nabla_G u) = w_2f(u) &\text{ in } \Omega,\\ u=0 &\text{ on } \partial\Omega, \end{cases}\end{equation*}$ \end{document} where \begin{document}$\Omega$
Phuong Le
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Liouville theorems for an integral equation of Choquard type
Communications on Pure and Applied Analysis, 2020 We establish sharp Liouville theorems for the integral equation \begin{document}$ u(x) = \int_{\mathbb{R}^n} \frac{u^{p-1}(y)}{|x-y|^{n-\alpha}} \int_{\mathbb{R}^n} \frac{u^p(z)}{|y-z|^{n-\beta}} dz dy, \quad x\in\mathbb{R}^n, $\end{document} where ...
Phuong Le
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Liouville theorems for ancient caloric functions via optimal growth conditions [PDF]
Proceedings of the American Mathematical Society, 2019 We provide some Liouville theorems for ancient nonnegative solutions of the heat equation on a complete non-compact Riemannian manifold with Ricci curvature bounded from below.
S. Mosconi
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Comparison and oscillation theorems for singular Sturm-Liouville operators [PDF]
Opuscula Mathematica, 2014 We prove analogues of the classical Sturm comparison and oscillation theorems for Sturm-Liouville operators on a finite interval with real-valued distributional potentials.
Monika Homa, Rostyslav Hryniv
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Liouville Theorems and a Schwarz Lemma for Holomorphic Mappings Between Kähler Manifolds [PDF]
Communications on Pure and Applied Mathematics, 2018 We derive some consequences of the Liouville theorem for plurisubharmonic functions of L.‐F. Tam and the author. The first result provides a nonlinear version of the complex splitting theorem (which splits off a factor of ℂ isometrically from the simply ...
Lei Ni
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Finite Morse index solutions of the Hénon Lane–Emden equation
Journal of Inequalities and Applications, 2019 In this paper, we are concerned with Liouville-type theorems of the Hénon Lane–Emden triharmonic equations in whole space. We prove Liouville-type theorems for solutions belonging to one of the following classes: stable solutions and finite Morse index ...
Abdellaziz Harrabi, Cherif Zaidi
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Complete Riemannian manifolds with Killing — Ricci and Codazzi — Ricci tensors
Дифференциальная геометрия многообразий фигур, 2022 The purpose of this paper is to prove of Liouville type theorems, i. e., theorems on the non-existence of Killing — Ricci and Codazzi — Ricci tensors on complete non-compact Riemannian manifolds.
S.E. Stepanov, I. I. Tsyganok, J. Mikeš
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Gradient estimates for a nonlinear parabolic equation and Liouville theorems [PDF]
Manuscripta mathematica, 2018 We establish local elliptic and parabolic gradient estimates for positive smooth solutions to a nonlinear parabolic equation on a smooth metric measure space.
Jia-Yong Wu
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Cotangent models for integrable systems [PDF]
, 2016 We associate cotangent models to a neighbourhood of a Liouville torus in symplectic and Poisson manifolds focusing on a special class called $b$-Poisson/$b$-symplectic manifolds.
Kiesenhofer, Anna, Miranda, Eva
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A new Definition of Fractional Derivative and Fractional Integral [PDF]
Kirkuk Journal of Science, 2018 In this paper, we introduce three different definitions of fractional derivatives, namely Riemann-Liouville derivative, Caputo derivative and the new formula Caputo expansion formula, and some basics properties of these derivatives are discussed.
Ahmed M. Kareem
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