ON SCHRÖDINGER EQUATIONS WITH INDEFINITE NONLINEARITIES
نویسندگان
چکیده
منابع مشابه
Discrete nonlinear Schrödinger equations with arbitrarily high-order nonlinearities.
A class of discrete nonlinear Schrödinger equations with arbitrarily high-order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrödinger equation and the Ablowitz-Ladik equation. As a common property, these equations possess three kinds of exact analytical sta...
متن کاملOn the Schrödinger Equation with Dissipative Nonlinearities of Derivative Type
which suggests dissipativity if Imλ < 0. In fact, it is proved in [17] that the solution decays like O((t log t)−1/2) in Lx as t → +∞ if Imλ < 0 and u0 is small enough. Since the non-trivial free solution (i.e., the solution to (1) for N ≡ 0, u0 = 0) only decays like O(t−1/2), this gain of additional logarithmic time decay reflects a disspative character. Now we turn our attentions to the gener...
متن کاملConcentration of homoclinic solutions for some fourth-order equations with sublinear indefinite nonlinearities
In this paper, we mainly explore the phenomenon of concentration of homoclinic solutions for a class of nonperiodic fourth-order equations with sublinear indefinite nonlinearities. The proof is based on variational methods.
متن کاملThe nonlinear Schrödinger equations with combined nonlinearities of power - type and Hartree - type ∗
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.
متن کاملOn Schrr Odinger Equations with Concentrated Nonlinearities
Schrr odinger equations with nonlinearities concentrated in some regions of space are good models of various physical situations and have interesting mathematical properties. We show that in the semiclassical limit it is possible to separate the relevant degrees of freedom by noticing that in the regions where the nonlinearities are eeective all states are suppressed but the metastable ones (re...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2009
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s000497270800110x