点阵图上一些不定非线性Schrödinger方程的基态解

IF 0.9 3区数学 Q2 MATHEMATICS

Acta Mathematica Sinica-English Series Pub Date : 2025-05-15 DOI:10.1007/s10114-025-3111-z

Wendi Xu

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引用次数: 0

摘要

本文考虑了格图N上具有不定变分泛函的Schrödinger型方程−Δu + V (x)u = f(x, u)，其中Δ为离散拉普拉斯式。具体地说，我们假设V (x)和f（x, u）在x中是周期性的，f满足某种生长条件，0位于（−Δ + V）的有限谱隙中。利用Pankov引入的广义Nehari流形的方法获得了基态解。

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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Ground State Solutions to Some Indefinite Nonlinear Schrödinger Equations on Lattice Graphs

In this paper, we consider the Schrödinger type equation −Δu + V (x)u = f(x, u) on the lattice graph ℤ^N with indefinite variational functional, where Δ is the discrete Laplacian. Specifically, we assume that V (x) and f(x, u) are periodic in x, f satisfies some growth condition and 0 lies in a finite spectral gap of (−Δ + V). We obtain ground state solutions by using the method of generalized Nehari manifold which has been introduced by Pankov.

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来源期刊

Acta Mathematica Sinica-English Series 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

138

审稿时长

14.5 months

期刊介绍： Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.