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Inverse spectral problem for the Sturm Liouville equation
Inverse Problems, 2003Summary: 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. +3 more
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Stability of solutions to Sturm-Liouville diffusion equations
Transport Theory and Statistical Physics, 1986Abstract Stability of solutions of abstract half-space problems of the type T ψ'1 (x)=-Aψ(x)(0> x > ∞) is established under perturbations of the resolvent of the (unbounded) positive self-adjoint operator A. Applications are given to Sturm-Liouville type diffusion equations.
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Sharp bounds of nodes for Sturm–Liouville equations
Monatshefte für MathematikzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hao Feng +3 more
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A SINGULAR STURM–LIOUVILLE EQUATION INVOLVING MEASURE DATA
Communications in Contemporary Mathematics, 2013Let α > 0 and let μ be a bounded Radon measure on the interval (-1, 1). We are interested in the equation -(|x|2αu′)′ + u = μ on (-1, 1) with boundary condition u(-1) = u(1) = 0. We identify an appropriate concept of solution for this equation, and we establish some existence and uniqueness results.
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Inverse problem for Sturm-Liouville and hill equations
Annali di Matematica Pura ed Applicata, 1987We 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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A Coupled System of Sturm–Liouville Differential Equations
Mathematical NotesIn this paper, the authors investigate the existence and the asymptotic behavior of positive continuous solutions of the following nonlinear coupled system: \[ \left\{ \begin{array}{c} -\frac{1}{A}(Au')'=a(x)u^pv^r \quad \text{on}\ (0,1)\\ -\frac{1}{B}(Bu')'=b(x)u^qv^s\quad \text{on}\ (0,1),\\ u(0)=u(1)=v(0)=v(1)=0, \end{array} \right. \] where \(p, q \
Belkahla, S., ZineElAbidine, Z.
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Sturm-Liouville equations involving discontinuous nonlinearities
2016This paper deals with equations of Sturm-Liouville-type having nonlinearities on the righthand side being possibly discontinuous. We present different existence results of such equations under various hypotheses on the nonlinearities. Our approach relies on critical point theory for locally Lipschitz functionals.
BONANNO, Gabriele +2 more
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