Non-real eigenvalues of nonlocal indefinite Sturm–Liouville problems

Abstract

Abstract The present paper deals with non-real eigenvalues of regular nonlocal indefinite Sturm–Liouville problems. The existence of non-real eigenvalues of indefinite Sturm–Liouville differential equation with nonlocal potential K ( x , t ) $K(x,t)$ associated with self-adjoint boundary conditions is studied. Furthermore, a priori upper bounds of non-real eigenvalues for a class of indefinite differential equation involving nonlocal point interference potential function is obtained.

Keywords

• Indefinite Sturm–Liouville problem
• Nonlocal potential
• Non-real eigenvalue
• A priori bounds