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, 2008 Regular and singular Sturm-Liouville problems (SLP) are studied including the continuous and differentiable dependence of eigenvalues on the problem.
Anton Zettl
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Sturm—Liouville problems and discontinuous eigenvalues
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1999If a Sturm—Liouville problem is given in an open interval of the real line, then regular boundary value problems can be considered on compact sub-intervals. For these regular problems, all with necessarily discrete spectra, the eigenvalues depend on both the end-points of the compact intervals, and upon the choice of the real separated boundary ...
Everitt, W. N., Möller, M., Zettl, A.
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The inverse Sturm–Liouville problem III
Communications on Pure and Applied Mathematics, 1984[For part II see ibid. 37, 1-11 (1984; Zbl 0552.58024).] We discuss the inverse spectral theory of the Sturm-Liouville problem \(- y''+q(x)y=\lambda y,\) with boundary conditions \(y(0)=0\), \(by(1)+y'(1)=0.\)
Dahlberg, Björn E. J. +1 more
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The inverse Sturm–Liouville problem. II
Communications on Pure and Applied Mathematics, 1984[Part I, cf. the first and the third author, ibid. 36, 767-783 (1983; Zbl 0507.58037).] - Let \(L^ 2\) be the Hilbert space of square- integrable real-valued functions on [0,1]. If \(q\in L^ 2\) and \((a,b)\in {\mathbb{R}}^ 2\) are fixed, then the Sturm-Liouville problem \(- y''+qy=\lambda y\), \(0\leq x\leq 1\), with boundary conditions a y(0)\(+y'(0)=
Isaacson, E. L. +2 more
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2015
The chapter provides an existence principle for the Sturm–Liouville boundary value problem with p (\(p \in \mathbb {N}\)) state-dependent impulse conditions Open image in new window Provided a, \(b \in [0,\infty )\), \(c_j \in \mathbb {R}\), \(j = 1,2\), and the data functions f, \(J_i\), \(M_i\), \(i=1,\ldots ,p\), are bounded ...
Irena Rachůnková, Jan Tomeček
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The chapter provides an existence principle for the Sturm–Liouville boundary value problem with p (\(p \in \mathbb {N}\)) state-dependent impulse conditions Open image in new window Provided a, \(b \in [0,\infty )\), \(c_j \in \mathbb {R}\), \(j = 1,2\), and the data functions f, \(J_i\), \(M_i\), \(i=1,\ldots ,p\), are bounded ...
Irena Rachůnková, Jan Tomeček
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Mathematical software for Sturm-Liouville problems
ACM Transactions on Mathematical Software, 1993Software is described for the Sturm-Liouville eigenproblem. Eigenvalues, eigenfunctions, and spectral density functions can be estimated with global error control. The method of approximating the coefficients forms the mathematical basis. The underlying algorithms are briefly described, and several examples are presented.
Steven Pruess, Charles T. Fulton
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1996
Let us consider the equation $$- \left( {p\left( x \right)y'\left( x \right)} \right)' + q\left( x \right)y\left( x \right) = \lambda p\left( x \right)y\left( x \right) $$ on the segment 0 ≤ x ≤ l, assuming that the real-valued functions p, p′,q, ρ are continuous on this segment and $$p\left( x \right) \geqslant p_0 > 0,p\left( x \right ...
Yuri Egorov, Vladimir Kondratiev
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Let us consider the equation $$- \left( {p\left( x \right)y'\left( x \right)} \right)' + q\left( x \right)y\left( x \right) = \lambda p\left( x \right)y\left( x \right) $$ on the segment 0 ≤ x ≤ l, assuming that the real-valued functions p, p′,q, ρ are continuous on this segment and $$p\left( x \right) \geqslant p_0 > 0,p\left( x \right ...
Yuri Egorov, Vladimir Kondratiev
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Sturm‐Liouville eigenvalue problems on networks
Mathematical Methods in the Applied Sciences, 1988AbstractThe description of heat conduction on ramified wires, for instance, leads to a Sturm‐Liouville eigenvalue problem on a network. It is shown that these problems are special canonical eigenvalue problems in the sense of Hölder, and therefore they can be investigated within the theory of S‐Hermitian eigenvalue problems.
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Stochastic nonhomogeneous sturm liouville problems
Journal of the Franklin Institute, 1966Abstract Nonhomogeneous boundary value problems of the Sturm-Liouville type having random forcing functions are considered. Estimates for the statistical moments of the response are found in the case that the forcing function is stationary and weakly correlated, thereby extending previous work having to do with stochastic initial value problems.
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Strongly Singular Sturm - Liouville Problems
Mathematische Nachrichten, 2001In the usual Sturm-Liouville theory, in order to use the spectral theorem for selfadjoint operators in Hilbert spaces, appropriate boundary conditions are used together with the Sturm-Liouville equation \[ -(ru'(x))'+ p(x) u(x)=\lambda m(x) u(x)\quad\text{on }(a,b) \] to form selfadjoint eigenvalue problems. For example, for the Fourier equation \(-u''=
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