The Existence of Solutions for a Class of Schrödinger Equations via Morse Index Theory

LI Jia-yang, WANG Qi

doi:10.13371/j.cnki.chin.q.j.m.2022.03.005

Chinese Quarterly Journal of Mathematics >

2022 , Vol. 37 >Issue 3: 274 - 280

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2022.03.005

The Existence of Solutions for a Class of Schrödinger Equations via Morse Index Theory

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1. School of Mathematics and Statistics, Henan University, Kaifeng 475004, China; 2. Department of
Mathematics, Shandong University, Jinan 250100, China

LI Jia-yang (1998-), female, native of Luoyang, Henan, graduate student of Henan University, engages in dynamic systems. WANG Qi (1982-) male, native of Luoyang, Henan, associate professor of Henan University, engages in nonlinear functional analysis.

Received date: 2021-11-29

Online published: 2022-09-19

Supported by

Supported by DEU of Henan (Grant No. 19A110011) and PSF of China (Grant No. 188576).

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Abstract

In this paper, with the relative Morse index, we will study the existence of
solutions of (1.1) under the assumptions that V satisfies some weaker conditions than
those in [2].

Key words： ; Relative Morse index; Morse theory; Schr?dinger equations

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LI Jia-yang, WANG Qi . The Existence of Solutions for a Class of Schrödinger Equations via Morse Index Theory[J]. Chinese Quarterly Journal of Mathematics, 2022 , 37(3) : 274 -280 . DOI: 10.13371/j.cnki.chin.q.j.m.2022.03.005

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