An inhomogeneous eigenvalue problem

An unusual eigenvalue problem

We discuss an eigenvalue problem which arises in the studies of asymptotic stability of a self-similar attractor in the sigma model. This problem is rather unusual from the viewpoint of the spectral theory of linear operators and requires special methods to solve it. One of such methods based on continued fractions is presented in detail and applied to determine the eigenvalues.

Inhomogeneous Two-Parameter Abstract Cauchy Problem

Inverse Problem for an Inhomogeneous Schrödinger Equation * †

Let (− k 2)u = −u + q(x)u − k 2 u = δ(x), x ∈ R, ∂u ∂|x| − iku → 0, |x| → ∞. Assume that the potential q(x) is real-valued and compactly supported: q(x) = q(x), q(x) = 0 for |x| ≥ 1, 1 −1 |q|dx < ∞, and that q(x) produces no bound states. Let u(−1, k) and u(1, k) ∀k > 0 be the data. Theorem.Under the above assumptions these data determine q(x) uniquely.

An Eigenvalue Problem for Elliptic Systems

By means of non-smooth critical point theory we prove existence of weak solutions for a general nonlinear elliptic eigenvalue problem under natural growth conditions .

On an Eigenvector-Dependent Nonlinear Eigenvalue Problem

We first provide existence and uniqueness conditions for the solvability of an algebraic eigenvalue problem with eigenvector nonlinearity. We then present a local and global convergence analysis for a self-consistent field (SCF) iteration for solving the problem. The well-known sin Θ theorem in the perturbation theory of Hermitian matrices plays a central role. The near-optimality of the local ...