Discrete Schrödinger equations and systems with mixed and concave-convex nonlinearities

IF 0.8 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society Pub Date : 2024-04-23 DOI:10.1090/proc/16834

Guanwei Chen, Shiwang Ma

引用次数: 0

Abstract

In this paper, we obtain the existence of at least two standing waves (and homoclinic solutions) for a class of time-dependent (and time-independent) discrete nonlinear Schrödinger systems or equations. The novelties of the paper are as follows. (1) Our nonlinearities are composed of three mixed growth terms, i.e., the nonlinearities are composed of sub-linear, asymptotically-linear and super-linear terms. (2) Our nonlinearities may be sign-changing. (3) Our results can also be applied to the cases of concave-convex nonlinear terms. (4) Our results can be applied to a wide range of mathematical models.

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具有混合和凹凸非线性的离散薛定谔方程和系统

在本文中，我们得到了一类与时间相关（和与时间无关）的离散非线性薛定谔系统或方程至少存在两个驻波（和同轴解）。本文的新颖之处如下。(1) 我们的非线性由三个混合增长项组成，即非线性由次线性、渐近线性和超线性项组成。(2) 我们的非线性可能是符号变化的。(3) 我们的结果也适用于凹凸非线性项的情况。(4) 我们的结果可应用于多种数学模型。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.