This theory is important in applied mathematics, where Sturm–Liouville problems occur very frequently, particularly when dealing with separable linear partial differential equations.

Jun 23, 2024 · Problems 1–4 of Section 11.1 are Sturm–Liouville problems. (Problem 5 isn’t, although some authors use a definition of Sturm-Liouville problem that does include it.)

The so-called Sturm-Liouville Problems de ne a class of eigenvalue problems, which include many of the previous problems as special cases. The S L Problem helps to identify those assumptions that are …

Problems satisfying the hypothesis of the theorem (including the “Moreover”) are called regular Sturm–Liouville problems, and we will only consider such problems here.

Regular and singular Sturm-Liouville problems (SLP) are studied including the continuous and di erentiable dependence of eigenvalues on the prob- lem.

If p(a) = p(b), p > 0 and r > 0 on [a, b], p, q, r are continuous functions on [a, b], then solving Sturm-Liouville equation (6.2) coupled with boundary conditions

If one of the coefficient functions in the operator L violates a condition in the definition of a regular Sturm–Liouville problem at an endpoint (e.g., if p(0) = 0, or if q(x) → ∞ as x → L), or if the interval is …