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We consider the equation $- {(r (x) y^{'} (x))}^{'} + q (x) y (x) = f (x), x \in ℝ (*)$ where $f \in L_{p} (ℝ)$ , $p \in (1, \infty)$ and $\begin{matrix} r > 0, q \geq 0, \frac{1}{r} \in L_{1}^{loc} (ℝ), q \in L_{1}^{loc} (ℝ), \\ lim_{| d | \to \infty} \int_{x - d}^{x} \frac{d t}{r (t)} \cdot \int_{x - d}^{x} q (t) d t = \infty . \end{matrix}$ In an earlier paper, we obtained a criterion for correct solvability of ( $*$ ) in $L_{p} (ℝ),$ $p \in (1, \infty) ...$

Minimality of the system of root functions of Sturm-Liouville problems with decreasing affine boundary conditions

Y. N. Aliyev (2007)

Colloquium Mathematicae

We consider Sturm-Liouville problems with a boundary condition linearly dependent on the eigenparameter. We study the case of decreasing dependence where non-real and multiple eigenvalues are possible. By determining the explicit form of a biorthogonal system, we prove that the system of root (i.e. eigen and associated) functions, with an arbitrary element removed, is a minimal system in L₂(0,1), except for some cases where this system is neither complete nor minimal.

Multiple positive solutions of Sturm-Liouville equations with singularities.

Wang, Zenggui, Liu, Lishan, Wu, Yonghong (2006)

Discrete Dynamics in Nature and Society

Nonclassical Sturm-Liouville problems and Schrödinger operators on radial trees.

Carlson, Robert (2000)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Nonlinear eigenvalue problems for fourth order ordinary differential equations

Jolanta Przybycin (1995)

Annales Polonici Mathematici

This paper was inspired by the works of Chiappinelli ([3]) and Schmitt and Smith ([7]). We study the problem ℒu = λau + f(·,u,u',u'',u''') with separated boundary conditions on [0,π], where ℒ is a composition of two operators of Sturm-Liouville type. We assume that the nonlinear perturbation f satisfies the inequality |f(x,u,u',u'',u''')| ≤ M|u|. Because of the presence of f the considered equation does not in general have a linearization about 0. For this reason the global bifurcation theorem of...

On an inverse scattering problem for a discontinuous Sturm-Liouville equation with a spectral parameter in the boundary condition.

Mamedov, Khanlar R. (2010)

Boundary Value Problems [electronic only]

On certain singular third order eigenvalue problem

Michal Greguš, Michal Greguš, Jr. (2003)

Archivum Mathematicum

In this paper a singular third order eigenvalue problem is studied. The results of the paper complete the results given in the papers [3], [5].

On certain third order eigenvalue problem

Michal Greguš (2000)

Archivum Mathematicum

On sampling expansions of Kramer type.

Poulkou, Anthippi (2004)

Abstract and Applied Analysis

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Displaying 61 – 80 of 142

Integrated density of states of self-similar Sturm–Liouville operators and holomorphic dynamics in higher dimension

Invariant transformations for the Sturm--Liouville operator.

Inverse nodal problems for the Sturm-Liouville differential operators on a star-type graph.

Inverse spectral problems for nonlinear Sturm-Liouville problems.

Irregular Sampling and the Inverse Spectral Problem.

Left-definite variations of the classical Fourier expansion theorem.

Methods of analysis of the condition for correct solvability in $L_{p} (ℝ)$ of general Sturm-Liouville equations

Minimality of the system of root functions of Sturm-Liouville problems with decreasing affine boundary conditions

Multiple positive solutions of Sturm-Liouville equations with singularities.

Nonclassical Sturm-Liouville problems and Schrödinger operators on radial trees.

Nonlinear eigenvalue problems for fourth order ordinary differential equations

Nonlinear eigenvalue problems with the parameter near resonance

Non-self-adjoint singular Sturm-Liouville problems with boundary conditions dependent on the eigenparameter.

Note on the absolutely continuous spectrum of Sturm-Liouville operators.

On a Lagrange problem and its generalizations

On a superlinear Sturm-Liouville equation and a related bouncing problem.

On an inverse scattering problem for a discontinuous Sturm-Liouville equation with a spectral parameter in the boundary condition.

On certain singular third order eigenvalue problem

On certain third order eigenvalue problem

On sampling expansions of Kramer type.

Currently displaying 61 – 80 of 142