Schrödinger-Maxwell equations driven by mixed local-nonlocal operators

IF 2.5 2区数学 Q1 MATHEMATICS

Fractional Calculus and Applied Analysis Pub Date : 2024-02-26 DOI:10.1007/s13540-024-00251-x

引用次数: 0

Abstract

In this paper we prove existence of solutions to Schrödinger-Maxwell type systems involving mixed local-nonlocal operators. Two different models are considered: classical Schrödinger-Maxwell equations and Schrödinger-Maxwell equations with a coercive potential, and the main novelty is that the nonlocal part of the operator is allowed to be nonpositive definite according to a real parameter. We then provide a range of parameter values to ensure the existence of solitary standing waves, obtained as Mountain Pass critical points for the associated energy functionals.

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由混合局部-非局部算子驱动的薛定谔-麦克斯韦方程

摘要本文证明了涉及本地-非本地混合算子的薛定谔-麦克斯韦方程组解的存在性。本文考虑了两种不同的模型：经典薛定谔-麦克斯韦方程和具有胁迫势的薛定谔-麦克斯韦方程，其主要新颖之处在于允许算子的非局部部分根据一个实参数为非正定。然后，我们提供了一系列参数值，以确保孤驻波的存在，并将其作为相关能量函数的山口临界点。

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

Fractional Calculus and Applied Analysis MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

16.70%

发文量

101

期刊介绍： Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.