Bounds of Eigenvalues for Complex <i>q</i>-Sturm–Liouville Problem

Abstract

The eigenvalues of complex q-Sturm–Liouville boundary value problems are the focus of this paper. The coefficients of the corresponding q-Sturm–Liouville equation provide the lower bounds on the real parts of all eigenvalues, and the real part of the eigenvalue and the coefficients of this q-Sturm–Liouville equation provide the bounds on the imaginary part of each eigenvalue.

Keywords

• complex q-Sturm–Liouville problem
• complex valued coefficient
• non-real eigenvalue
• upper bounds
• lower bounds