In this paper we study superlinear elliptic systems in Hamiltonian form. Using an Orlicz-space setting, we extend the notion of critical growth to superlinear nonlinearities which do not have a polynomial growth. Existence of nontrivial solutions is proved for superlinear nonlinearities which are subcritical in this generalized sense.

This paper is devoted to a comprehensive study of the nonlinear Schrödinger equations with combined nonlinearities of the power-type and Hartree-type in any dimension n ≥ 3. With some structural conditions, a nearly whole picture of the interactions of these nonlinearities in the energy space is given. The method is based on the Morawetz estimates and perturbation principles.

Abstract We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on eigenvector, or several eigenvectors (or their corresponding invariant subspace). The are derived from an implicit viewpoint. More precisely, we change Newton update equation in a way that next iterate does not only appear linearly equation. Although modifications of make methods implic...

The anomalous transmission properties of zero-permittivity ultranarrow channels are used to boost Kerr nonlinearities and achieve switching and bistable response for moderate optical intensities. Strong field enhancement, uniform all along the channel, is a typical feature of ε-near-zero supercoupling and is shown to be particularly suited to enhance nonlinear effects. This is obtained by desig...

Although mammalian vocalizations are predominantly harmonically structured, they can exhibit an acoustic complexity with nonlinear vocal sounds, including deterministic chaos and frequency jumps. Such sounds are normative events in mammalian vocalizations, and can be directly traceable to the nonlinear nature of vocal-fold dynamics underlying typical mammalian sound production. In this study, w...