The distribution of the eigenvalues for second order eigenvalue problems in the presence of an arbitrary number of turning points

Indefinite Eigenvalue Problems with Several Singular Points and Turning Points

“…This paper continues the investigations made by Eberhard, Freiling and Schneider (see [6], [7], [8]) who considered (1.1) in the case of several zeros of φ 2 and a bounded and integrable function χ; it contains and extends the main results of the dissertation [24] of the third author, written under the guidance of the two first authors.…”

On the Eigenvalues of Half-Linear Boundary Value Problems

“…(i) In the linear case Mingarelli [15] has proved the estimate (2.6) in the form kπ[1+o (1)] for k → ∞ but for a wider class of functions q(t). If the eigenvalue problem (1.1) -(1.2) is linear and regular (but not necessarily selfadjoint), then (2.6) has been derived by Eberhard and Freiling [8] under the same restrictions on q(t). In the half -linear case (2.6) has been proved by Elbert [9] under assumptions q(t) > 0, q(t) continuous but not requiring the differentiability of q(t).…”

Existence and Asymptotics of Eigenvalues of Indefinite Systems of Sturm–Liouville and Dirac Type

“…Again, better asymptotics are available if the coefficients are more restricted, cf. [5], [6]. There are also results on the case where r>0 and s is indefinite, cf.…”