Multiplicities and relative position of eigenvalues of a quadratic pencil of Sturm-Liouville operators

Asymptotic behavior of the solutions and nodal points of Sturm-Liouville differential expressions

“…Differentiating (20) with respect to x and repeating the technique use in the proof of (6), involving Lemma 1, we obtain (7). Theorem 1 is proved.…”

“…Given any fixed representative q ∈ L[0, π], by the Riemann-Lebesgue Lemma and the integral representation (20), the estimate of the approximation error in (6) has the form…”

“…Using the integral representation (20) and estimate (19) with ρ λ ≡ π q C[0,π] ≤ π as ρ λ , as in [7, Chapter 1, § 2, Lemma 2.2], we conclude the existence of a constant B = B(q) depending only on the norm of the potential q in C[0, π] such that y(x, λ n j k ) − cos √ λ n j k x − β(x, λ n j k ) sin √ λ n j k x √ λ n j k…”

“…To the study of Sturm-Liouville operators with potential depending on the spectral parameter, we may also relate the cycle of works devoted to the sheaves of differential operators (for example, see [19,20]). …”

An inverse nodal problem for differential pencils with complex spectral parameter dependent boundary conditions

“…Some aspects of this type problems were studied by many authors (see [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38]). Such problems play an important role in mathematics and have many applications in natural sciences and engineering.…”