Soliton solutions for a quasilinear Schrödinger equation via Morse theory

Proceedings Mathematical Sciences

Duchao Liu²  Peihao Zhao¹ 

[1] $$;School of Mathematics and Statistics, Lanzhou University, Lanzhou 0000, People’s Republic of China$$

关键词: Quasilinear Schrödinger equation;    soliton solution;    critical point;    Morse theory;    local linking.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In this paper, Morse theory is used to show the existence of nontrivial weak solutions to a class of quasilinear Schrödinger equation of the form$$-𝛥 u - frac{p}{2^{p-1}} u 𝛥_p (u^2) = f(x, u)$$in a bounded smooth domain $𝛺 subset mathbb{R}^N$ with Dirichlet boundary condition.

【 授权许可】

Unknown