The Lyapunov exponents associated with nonlinear electronic circuits are related to the earlier introduced dynamic eigenvalues.

The nonlinear eigenvalue problem of the differential equation ( |x′|p−2 x′ )′ + (λ+ c(t)) |x|p−2 x = 0, p > 1, with respect to the periodic boundary conditions: x(0) = x(T ), x′(0) = x′(T ), or to the antiperiodic boundary conditions: x(0) = −x(T ), x′(0) = −x′(T ) are considered. Various results on the set of eigenvalues concerning both problems are presented. Some estimates are given for the ...

Variational principles are very powerful tools when studying self-adjoint linear operators on a Hilbert spaceH. Bounds for eigenvalues, comparison theorems, interlacing results and monotonicity of eigenvalues can be proved easily with these characterizations, to name just a few. In this paper we consider generalization of these principles to families of linear, self-adjoint operators depending ...

Motivated by extremal problems of weighted Dirichlet or Neumann eigenvalues, we will establish two fundamental results on the dependence of weighted eigenvalues of the one-dimensional p-Laplacian on indefinite integrable weights. One is the continuous differentiability of eigenvalues in weights in the Lebesgue spaces L with the usual norms. Another is the continuity of eigenvalues in weights wi...