Further spectral properties of uniformly elliptic operators that include a non-local term (Q2479194)

The author presents a detailed study of the eigenvalues of \(L_\varepsilon=A+\varepsilon B\), where \(A\) is a uniformly elliptic operator on a bounded connected subset of \(\mathbb{R}^n\) and \(B\) is a rank one integral operator. For selfadjoint \(B\) the variation, monotonicity, and \(\varepsilon\to\pm\infty\) asymptotics of the \(i\)-th eigenvalue are studied by means of plots as well as qualitative theorems. For nonselfadjoint \(B\) plots of real as well as complex eigenvalues (including merging real eigenvalues which then move off the axis) are presented and the monotonicity of the real part of the \(i\)-th eigenvalue as a function of \(\varepsilon\) is proved.