Principal eigenvalues of a class of nonlinear integro-differential operators

Absence of Eigenvalues for Integro-differential Operators with Periodic Coefficients

The absence of the point spectrum for some nonselfadjoint integrodifferential operators is investigated by applying perturbation theory methods. The considered differential operators could be of any order and are assumed to act in Lp(R+) or Lp(R) (1 ≤ p < ∞). Finally, as an application of general results, some spectral properties of the perturbed Hill operator are derived.

Numerical methods for a class of nonlinear integro-differential equations

In a previous article (Glowinski, J. Math. Anal. Appl. 41, 67–96, 1973) the first author discussed several methods for the numerical solution of nonlinear equations of the integro-differential type with periodic boundary conditions. In this article we discuss an alternative methodology largely based on the Strang’s symmetrized operator-splitting scheme. Several numerical experiments suggest tha...

Nonlinear Integro - Differential Equations

On a class of integro-differential problems

a class of fourth order differential operators with transmission conditions

we investigate a class of fourth-order differential operators with eigenparameter dependent boundary conditions and transmission conditions. a self-adjoint linear operator a is defined in a suitable hilbert space h such that the eigenvalues of such a problem coincide with those of a . we discuss asymptotic behavior of its eigenvalues and completeness of its eigenfunctions. finally, we obtain th...