Results 161 to 170 of about 8,236 (196)

Inverse spectral problem for the Sturm Liouville equation

Inverse Problems, 2003
Summary: This paper discusses a new numerical approach to computing the potential \(q\) in the Sturm-Liouville problem \(-y''+ qy=\lambda y\) on a compact interval. It is shown that an algorithm to recover \(q\) from eigenvalues and multiplier constants can be derived. Examples of some test problems, and questions of efficiency are discussed.
Brown, B. M., Samko, V. S., Knowles, I. W., Marletta, M.   +3 more
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An Inverse Sturm‐Liouville Problem by Three Spectra

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1998
AbstractIt is well known that the equation of small transverse vibrations of a smooth string may be reduced by means of Liouville transform [1] to the Sturm‐Liouville equation. Then the inverse problem, i. e. determination of the potential, may be solved by given spectra of two boundary problems [2, 3, 4].
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Boundary value method for inverse Sturm–Liouville problems

Applied Mathematics and Computation, 2009
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Kammanee, Athassawat, Böckmann, Christine   +1 more
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Vectorial Inverse Sturm–Liouville Problem With Local Derivative

Mathematical Methods in the Applied Sciences
ABSTRACTThis study provides proof of the Ambarzumyan theorem for the ‐dimensional vectorial Sturm–Liouville problem. In defining the problem, we applied local derivative which is conformable. Notably, we observed that the multiplicity of eigenvalues is n in this problem.
Songul Tutuncu, H.Kemaloglu Koyunbakan, Yildiz Emul   +2 more
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Inverse Sturm–Liouville problems for non-Borg conditions

Journal of Inverse and Ill-posed Problems, 2019
Abstract We consider Sturm–Liouville problems on the finite interval with non-Borg conditions. Using eigenvalues of four Sturm–Liouville problems, we construct the spectral data and show that the mapping from potential to spectral data is a bijection. Moreover, we obtain estimates of spectral data in terms of potentials.
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Inverse problem for Sturm-Liouville and hill equations

Annali di Matematica Pura ed Applicata, 1987
We discuss the inverse Sturm-Liouville problem on a finite interval by the method of transformation kernel. The \(\tau\)-function, the Fredholm determinant of the transformation kernel, is explicitly written down in terms of the spectral data, from which a very explicit representation formula for the potential is deduced, and well-posedness of the ...
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Inverse Sturm-Liouville problems with homogeneous delay

Siberian Mathematical Journal, 2014
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Pikula, M. T., Vladičić, V. M., Nedić, D. D.   +2 more
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Lq -inverse spectral problems for semilinear Sturm–Liouville problems

Nonlinear Analysis: Theory, Methods & Applications, 2008
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Inverse bifurcation problems for nonlinear Sturm–Liouville problems

Inverse Problems, 2011
We consider the inverse nonlinear eigenvalue problems for the equation which is motivated biologically by the problem of population dynamics. It is assumed that f(u) is an unknown nonlinear term. Under the standard growth conditions on f, for any given ?
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Inverse Sturm-Liouville problems with two discontinuities

Inverse Problems, 1985
We consider the inverse problem for a Sturm-Liouville equation with two interior discontinuities. We assume that the potential is known in half the interval and that one boundary condition is given. We then show that the eigenvalues uniquely determine the potential in the whole interval and the other boundary condition, as well as the positions of and ...
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