The eigenvalue problem for a one-dimensional differential operator with a variable coefficient and nonlocal integral conditions

Abstract

We consider conditions for the existence of the eigenvalue λ = 0 in the eigenvalue problem for a differential operator with a variable coefficient and integral conditions. We analyze how these conditions depend on such properties of the coefficient p(x) as monotonicity and symmetry and observe some other properties of the spectrum of the eigenvalue problem. Particularly, we show by a numerical experiment that the fundamental theorem on the increase of the eigenvalues in the case of increasing coefficient p(x) is not valid for the eigenvalue problem with nonlocal conditions.