Results 1 to 10 of about 262 (118)
On partial fractional Sturm–Liouville equation and inclusion [PDF]
Advances in Difference Equations, 2021 AbstractThe Sturm–Liouville differential equation is one of interesting problems which has been studied by researchers during recent decades. We study the existence of a solution for partial fractional Sturm–Liouville equation by using the α-ψ-contractive mappings. Also, we give an illustrative example.
Zohreh Zeinalabedini Charandabi +3 more
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THE NEW ASYMPTOTICS FOR SOLUTIONS OF THE STURM–LIOUVILLE EQUATION
Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, 2023 Summary: In this paper, we show the development of a method that allows one to construct asymptotics for solutions to ordinary differential equations of arbitrary order with oscillating coefficients on the semiaxis. The idea of the method is presented on the example of studying the asymptotics of the Sturm-Liouville equation solutions.
Nazirova, Elvira A. +2 more
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The Sturm-Liouville Hierarchy of Evolution Equations
Advanced Nonlinear Studies, 2011 Abstract We introduce a hierarchy of evolution equations based on the Sturm-Liouville equation −(pφ′)′ + qφ = λyφ. Our hierarchy includes the Korteweg-de Vries (K-dV) and the Camassa-Holm (CH) hierarchy. We determine a class of solutions of the hierarchy which are of algebro-geometric type.
JOHNSON, RUSSELL ALLAN, L. Zampogni
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The Sturm-Liouville Hierarchy of Evolution Equations II
Advanced Nonlinear Studies, 2012 Abstract In a previous paper [15] we introduced the Sturm-Liouville (SL) hierarchy of evolution equations. This hierarchy includes the Korteveg-de Vries (K-dV) and the Camassa-Holm (CH) hierarchies. We also defined and discussed in detail the algebro-geometric solutions of the SL-hierarchy.
JOHNSON, RUSSELL ALLAN, L. Zampogni
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Reflectionless Sturm–Liouville equations
Journal of Computational and Applied Mathematics, 2007 We consider compactly supported perturbations of periodic Sturm-Liouville equations. In this context, one can use the Floquet solutions of the periodic background to define scattering coefficients. We prove that if the reflection coefficient is identically zero, then the operators corresponding to the periodic and perturbed equations, respectively, are
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On Sturm–Liouville equations with several spectral parameters [PDF]
Boletín de la Sociedad Matemática Mexicana, 2015 We give explicit formulas for a pair of linearly independent solutions of $(py')'(x)+q(x)=(λ_1r_1(x)+\cdots+λ_dr_d(x))y(x)$, thus generalizing to arbitrary $d$ previously known formulas for $d=1$. These are power series in the spectral parameters $λ_1,\dots,λ_d$ (real or complex), with coefficients which are functions on the interval of definition of ...
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On a fractional hybrid version of the Sturm–Liouville equation [PDF]
Advances in Difference Equations, 2020 AbstractIt is well known that the Sturm–Liouville equation has many applications in different areas of science. Thus, it is important to review different versions of the well-known equation. The technique of α-admissible α-ψ-contractions was introduced by Samet et al. in (Nonlinear Anal. 75:2154–2165, 2012).
Zohreh Zeinalabedini Charandabi +2 more
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On an inverse problem for Sturm-Liouville equation
, 2016 In this study, the theorem on necessary and sufficient conditions for the solvability of inverse problem for Sturm-Liouville operator with discontinuous coefficient is proved and the algorithm of reconstruction of potential from spectral data (eigenvalues and normalizing numbers) is given.
Karahan, Done, Mamedov, Khanlar R.
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Sturm-Liouville Equations with Besicovitch Almost-Periodicity [PDF]
Proceedings of the American Mathematical Society, 1989 In this article we extend a former result [Proc. Amer. Math. Soc. 97 , (1986), 269-272] dealing with the oscillation of (Bohr) almost-periodic Sturm-Liouville operators to the generalization of such as considered by Besicovitch.
Dzurnak, A., Mingarelli, A. B.
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Weight Summability of Solutions of the Sturm–Liouville Equation
Journal of Differential Equations, 1999 Let \(G(x,t)\) be the Green function of the equation \[ -y''(x)+q(x)y(x)=f(x),\;\;x\in \mathbb{R}, \tag{1} \] with \(f(x)\in L_{p}(\mathbb{R})\), \(p\in [1,\infty]\) (\(L_{\infty}(\mathbb{R}):=C(\mathbb{R})\)) and \(1\leq q(x)\in L_{1}^{\text{loc}}(\mathbb{R})\).
Chernyavskaya, N, Shuster, L
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