Inverse Sturm-Liouville problems with fixed boundary conditions
Electronic Journal of Differential Equations, 2015 Necessary and sufficient conditions for two sequences $\{\mu_n\}_{n=0}^\infty$ and $\{ a_n\}_{n=0}^\infty$ to be the spectral data for a certain Sturm-Liouville problem are well known.
Yuri A. Ashrafyan, Tigran N. Harutyunyan
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Inverse spectral problems for nonlinear Sturm-Liouville problems
Electronic Journal of Differential Equations, 2007 Summary: This paper concerns the nonlinear Sturm-Liouville problem \[ -u''(t) + f(u(t)) = \lambda u(t), \quad u(t) > 0, \quad t \in I := (0, 1), \quad u(0) = u(1) = 0, \] where \(\lambda \) is a positive parameter. We try to determine the nonlinear term \(f(u)\) by means of the global behavior of the bifurcation branch of the positive solutions in ...
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