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Weak Liouville-Arnold Theorems & Their Implications [PDF]
Communications in Mathematical Physics, 2012 This paper studies the existence of invariant smooth Lagrangian graphs for Tonelli Hamiltonian systems with symmetries. In particular, we consider Tonelli Hamiltonians with n independent but not necessarily involutive constants of motion and obtain two ...
A. Fathi +27 more
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A new kind of uniqueness theorems for inverse Sturm-Liouville problems [PDF]
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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Liouville Theorem for Dunkl Polyharmonic Functions [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2008 Assume that $f$ is Dunkl polyharmonic in $mathbb{R}^n$ (i.e. $(Delta_h)^p f=0$ for some integer $p$, where $Delta_h$ is the Dunkl Laplacian associated to a root system $R$ and to a multiplicity function $kappa$, defined on $R$ and invariant with respect ...
Guangbin Ren, Liang Liu
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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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AIMS Mathematics, 2023 The main purpose of this manuscript is to investigate the Sturm-Liouville BVP for non-autonomous Lagrangian systems. Under the suitable assumptions, we establish an existence theorem for three nonnegative solutions via Bonanno-Candito's three critical ...
Zhongqian Wang +2 more
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Harnack inequality and Liouville-type theorems for Ornstein-Uhlenbeck and Kolmogorov operators
Mathematics in Engineering, 2020 We prove, with a purely analytic technique, a one-side Liouville theorem for a class of Ornstein--Uhlenbeck operators ${\mathcal L_0}$ in $\mathbb{R}^N$, as a consequence of a Liouville theorem at “$t=- \infty$” for the corresponding Kolmogorov ...
Alessia E. Kogoj +2 more
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Boundary Value Problems, 2021 In this article, we consider the existence of solutions to the Sturm–Liouville differential equation with random impulses and boundary value problems.
Zihan Li, Xiao-Bao Shu, Tengyuan Miao
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Axioms, 2020 In this paper, we study the existence of solutions for nonlocal single and multi-valued boundary value problems involving right-Caputo and left-Riemann–Liouville fractional derivatives of different orders and right-left Riemann–Liouville fractional ...
Ahmed Alsaedi +3 more
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Sharp Liouville Theorems [PDF]
Advanced Nonlinear Studies, 2020 Abstract Consider the equation div (
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Liouville Theorems for Fractional Parabolic Equations [PDF]
Advanced Nonlinear Studies, 2021 Abstract In this paper, we establish several Liouville type theorems for entire solutions to fractional parabolic equations. We first obtain the key ingredients needed in the proof of Liouville theorems, such as narrow region principles and maximum principles for antisymmetric functions in unbounded domains, in which we remarkably weaken
Chen Wenxiong, Wu Leyun
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