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Some Liouville theorems and applications [PDF]
arXiv, 2006 We give exposition of a Liouville theorem established in \cite{Li3} which is a novel extension of the classical Liouville theorem for harmonic functions. To illustrate some ideas of the proof of the Liouville theorem, we present a new proof of the classical Liouville theorem for harmonic functions. Applications of the Liouville theorem, as well as that
Yanyan Li
arxiv +3 more sources
A general Liouville type theorem for some conformally invariant fully nonlinear equations [PDF]
arXiv, 2003 We establish a general Liouville type theorem for conformally invariant fully nonlinear equations.
Aobing Li, Yanyan Li
arxiv +3 more sources
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
doaj +2 more sources
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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
doaj +1 more source
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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Numerical Linear Algebra with Applications, Volume 30, Issue 1, January 2023., 2023 Abstract In this work, we focus on a fractional differential equation in Riesz form discretized by a polynomial B‐spline collocation method. For an arbitrary polynomial degree p$$ p $$, we show that the resulting coefficient matrices possess a Toeplitz‐like structure. We investigate their spectral properties via their symbol and we prove that, like for
Mariarosa Mazza +3 more
wiley +1 more source