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Sturm-Liouville theory for the radial $\Delta_p$ -operator
Mathematische Zeitschrift, 1998Let \(s^{(p)}=| s| ^{p-1}s\) (\(s\) real). The differential operator \[ L_p^\alpha=r^{-\alpha}\bigl(r^\alpha{u'}^{p-1}\bigr)' \] is considered, where \(s\) is the independent variable, \(\alpha\geq 0\), and \(p>1\). For \(\alpha=n-1\) and \(r=| x| \), this is the radial \(\Delta_p\)-operator in \(\mathbb{R}^n\).
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Nonlinear Sturm–Liouville Theory
2014In the next chapter, we’ll apply the Krasnoselskii-Rabinowitz bifurcation theorem in a very specific way: to the Euler buckling problem. The buckling problem belongs to an important class of problems in ordinary differential equations called nonlinear Sturm-Liouville problems.
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Classical Sturm Liouville expansion theory.
1953The idea of expanding a function in terms of the solutions of a second-order differential equation was first presented in a paper by Sturm and Liouville in 1836. But they gave a proof which is now not accepted. The first satisfactory proofs were not constructed until early in the twentieth century.
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Relative oscillation theory and essential spectra of Sturm–Liouville operators
Journal of Mathematical Analysis and Applications, 2023Gerald Teschl +2 more
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Relative oscillation theory for Sturm–Liouville operators extended
Journal of Functional Analysis, 2008Gerald Teschl, Helge Kruger
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