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Weak Liouville-Arnol′d Theorems and 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 theorems reminiscent of the Liouville-Arnold theorem.
Butler, L. T, SORRENTINO, ALFONSO
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Quantum gravity from timelike Liouville theory
Journal of High Energy Physics, 2019 A proper definition of the path integral of quantum gravity has been a long- standing puzzle because the Weyl factor of the Euclidean metric has a wrong-sign kinetic term.
Teresa Bautista +2 more
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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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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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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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Demonstratio Mathematica, 2023 In this article, we introduce and study a new class of hybrid fractional qq-integro-difference equations involving Riemann-Liouville qq-derivatives, supplemented with nonlocal boundary conditions containing Riemann-Liouville qq-integrals of different ...
Alsaedi Ahmed +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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Journal of Mathematics, 2021 We deal with the following Sturm–Liouville boundary value problem: −Ptx′t′+Btxt=λ∇xVt,x, a.e. t∈0,1x0cos α−P0x′0sin α=0x1cos β−P1x′1sin β=0 Under the subquadratic condition at zero, we obtain the existence of two nontrivial solutions and infinitely ...
Dan Liu, Xuejun Zhang, Mingliang Song
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