Schrödinger equation with asymptotically linear nonlinearities

نویسندگان

چکیده

LRES, Faculty of Sciences Tunis, University Tunis El Manar, Tunisia EM [email protected] KW Asymptotically linear % variational method Schr?dinger equations Cerami sequence KR nema In this paper, we investigate a quasilinear problem under Dirichlet boundary condition in regular domain with asymptotically nonlinearities. We use version the mountain pass theorem to prove existence solution without using Ambrosetti-Rabionovitz or any its refinements. Then, that same techniques work when nonlinearity is superlinear and subcritical at infinity.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On 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 کامل

Multiple Solutions for Biharmonic Equations with Asymptotically Linear Nonlinearities

Ruichang Pei1, 2 1 Center for Nonlinear Studies, Northwest University, Xi’an 710069, China 2 Department of Mathematics, Tianshui Normal University, Tianshui 741001, China Correspondence should be addressed to Ruichang Pei, [email protected] Received 26 February 2010; Revised 2 April 2010; Accepted 22 April 2010 Academic Editor: Kanishka Perera Copyright q 2010 Ruichang Pei. This is an open access ...

متن کامل

On Non - Linear Schrödinger Equation with Magnetic Field

We study the non-linear Schödinger equation with time depending magnetic field without smallness assumption at infinity. We obtain some results on the Cauchy problem, WKB asymptotics and instability.

متن کامل

Continuous and discrete Schrödinger systems with parity-time-symmetric nonlinearities.

We investigate the dynamical behavior of continuous and discrete Schrödinger systems exhibiting parity-time (PT) invariant nonlinearities. We show that such equations behave in a fundamentally different fashion than their nonlinear Schrödinger counterparts. In particular, the PT-symmetric nonlinear Schrödinger equation can simultaneously support both bright and dark soliton solutions. In additi...

متن کامل

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 کامل

ذخیره 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: Filomat

سال: 2022

ISSN: ['2406-0933', '0354-5180']

DOI: https://doi.org/10.2298/fil2202629e