Results 171 to 180 of about 5,326 (220)

Variational techniques for a system of Sturm–Liouville equations

Journal of Elliptic and Parabolic Equations, 2023
The paper is concerned with the sixth order Sturm-Liouville problem \[ \begin{cases} -\left(p_i(x)u_i'''(x)\right)'''+\left(q_i(x)u_i''(x)\right)''-\left(r_i(x)u_i'(x)\right)'+s_i(x)u_i(x) =\lambda F_{u_i}(x,u_1,\dots,u_n)\\ \text{ for } 00\) and \[ \max\left\{-\frac{q_i^- T^2}{\pi^2},-\frac{q_i^- T^2}{\pi^2}-\frac{r_i^- T^4}{\pi^4},-\frac{q_i^- T^2 ...
Saeid Shokooh
exaly   +2 more sources

Application of the Fractional Sturm–Liouville Theory to a Fractional Sturm–Liouville Telegraph Equation

Complex Analysis and Operator Theory, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ferreira, M., Rodrigues, M. Manuela, Vieira, Nelson   +2 more
openaire   +4 more sources

Conformable fractional Sturm‐Liouville equation

Mathematical Methods in the Applied Sciences, 2019
In this article, we discuss a conformable fractional Sturm‐Liouville boundary‐value problem. We prove an existence and uniqueness theorem for this equation and formulate a self‐adjoint boundary value problem. We also construct the associated Green function of this problem, and we give the eigenfunction expansions. Finally, we will give some examples.
Bilender P. Allahverdiev, Hüseyin Tuna, Yüksel Yalçinkaya   +2 more
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Sturm–Liouville equations

2020
A simple example of a formally symmetric differential equation, corresponding to M being real of order two and # order zero, is given by the general Sturm–Liouville ...
Christer Bennewitz, Malcolm Brown, Rudi Weikard   +2 more
openaire   +1 more source

Eigencurves for Two-Parameter Sturm-Liouville Equations

SIAM Review, 1996
The authors study the two-parameter Sturm-Liouville eigenvalue problem \[ -(p(x)y')'+q(x)y=(\lambda r(x)+ \mu)y,\quad a\leq x\leq b \] with separated boundary conditions \[ \cos(\alpha)y(a)-\sin(\alpha)p(a)y'(a)= 0, \qquad \cos(\beta)y(b)-\sin(\beta)p(b)y'(b)=0, \] where \(p(x)\) is continuously differentiable and positive on \([a,b]\), and \(q\) and \(
Paul Binding, Hans Volkmer
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The uniqueness of the solution of dual equations of an inverse indefinite Sturm–Liouville problem

Journal of Mathematical Analysis and Applications, 2005
In this paper we consider a linear second-order equation of Sturm–Liouville type: (I)y″+(λt−q(t))y=0,−1⩽t⩽1, with Dirichlet boundary conditions y(−1)=y(1)=0, where q is a positive sufficiently smooth function on [−1,1] and λ is a real parameter.
Hossein Kheiri, A Jodayree Akbarfam, Angelo B Mingarelli   +2 more
exaly   +2 more sources

A note on the equivalence between even order Sturm–Liouville equations and symplectic systems on time scales

Applied Mathematics Letters, 2013
The 2nth-order Sturm–Liouville differential and difference equations can be written as linear Hamiltonian differential systems and symplectic difference systems, respectively.
Petr Zemanek
exaly   +2 more sources

Spectral Asymptotics for Sturm-Liouville Equations

Proceedings of the London Mathematical Society, 1989
The author gives a detailed interesting survey on asymptotic formulas for various spectral characteristics of the general Sturm-Liouville problem \(-(pu')'+qu=\lambda wu\) under very mild conditions on the coefficients p,q, and w. Such spectral quantities are, for instance, the eigenvalue distribution, Green's function, the spectral function, and the ...
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Transformation of Sturm - Liouville differential equations

Functional Analysis and Its Applications, 1982
Translation from Funkts. Anal. Prilozh. 16, No.3, 42-44 (Russian) (1982; Zbl 0565.34035).
openaire   +1 more source