薛定谔方程及薛定谔-麦克斯韦方程的多解

毛安民, 李安然

数学学报 ›› 2012, Vol. 55 ›› Issue (3) : 425-436.

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PDF(432 KB)
数学学报 ›› 2012, Vol. 55 ›› Issue (3) : 425-436. DOI: 10.12386/A2012sxxb0040
论文

薛定谔方程及薛定谔-麦克斯韦方程的多解

    毛安民1, 李安然2
作者信息 +

Multiplicity of Solutions for a Non-periodic Schrödinger Equation and a Superlinear Schrödinger-Maxwell Equation

    An Min MAO1, An Ran LI2
Author information +
文章历史 +

摘要

不作周期性和对称性的假设,也没有Ambrosetti-Rabinowitz增长控制条件,我们得到了一类超线性薛定谔方程在全空间中无穷多解的存在性结果.同时,得到了一类超线性薛定谔-麦克斯韦方程无穷多解的存在性结果.

Abstract

Without the periodity and symmetricity, we present new results on the existence of infinitely solutions for some nonlinear superlinear Schrödinger equation in the entire space without Ambrosetti-Rabinowitz growth condition. Also, we get the existence of infinitely many large energy solutions for some superlinear Schrödinger- Maxwell equations.

关键词

薛定谔方程 / 薛定谔-麦克斯韦方程 / 喷泉定理

Key words

Schrödinger equation / Schrödinger-Maxwell equation / fountain theorem

引用本文

导出引用
毛安民, 李安然. 薛定谔方程及薛定谔-麦克斯韦方程的多解. 数学学报, 2012, 55(3): 425-436 https://doi.org/10.12386/A2012sxxb0040
An Min MAO, An Ran LI. Multiplicity of Solutions for a Non-periodic Schrödinger Equation and a Superlinear Schrödinger-Maxwell Equation. Acta Mathematica Sinica, Chinese Series, 2012, 55(3): 425-436 https://doi.org/10.12386/A2012sxxb0040

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基金

国家自然科学基金资助项目(10801088), 山东省自然科学青年基金项目(Q2007A02)
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