Abstract
The paper is concerned with eigenvalues of complex Sturm-Liouville boundary value problems. Lower bounds on the real parts of all eigenvalues are given in terms of the coefficients of the corresponding equation and the bound on the imaginary part of each eigenvalue is obtained in terms of the coefficients of this equation and the real part of the eigenvalue.
Highlights
If λ is an eigenvalue of (1) and (2),
Which, together with (13) and (21), implies that (8) holds for every eigenvalue λ with Re λ ≤ 0
The following corollary is a direct consequence of Theorem 1
Summary
If λ is an eigenvalue of (1) and (2), If λ is an eigenvalue of (1) and (2), with Re λ ≤ 0, where ε1 > 0 satisfies 8‖q1−‖21m1(ε1) < 1; and if λ is an eigenvalue of (1) and (2), with Re λ > 0, We first consider the case where λ is an eigenvalue of (1) and (2), with Re λ ≤ 0. From Re λ ≤ 0 and (12), it follows that
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