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Existence ground state solutions for a quasilinear Schrödinger equation with Hardy potential and Berestycki–Lions type conditions
Applied Mathematics Letters ( IF 2.9 ) Pub Date : 2021-08-25 , DOI: 10.1016/j.aml.2021.107615
Die Hu 1 , Qi Zhang 1
Affiliation  

In this paper, we discuss the quasilinear Schrödinger equation with a Hardy potential Δu+V(x)uμu|x|2Δ(u2)u=g(u),xRN{0},where N3, 0μ<μ̄=(N2)24, 1|x|2 is called the Hardy potential. By using Jeanjean’s monotonicity trick, we admit a class of ground state solutions for the above problem, under the general Berestycki–Lions type assumptions on the nonlinearity g, as well as some weak assumptions on the potential V.



中文翻译:

具有哈代势和 Berestycki-Lions 类型条件的拟线性薛定谔方程的存在基态解

在本文中,我们讨论了具有 Hardy 势的拟线性薛定谔方程 -Δ+(X)-μ|X|2-Δ(2)=G(),X电阻N{0},在哪里 N3, 0μ<μ̄=(N-2)24, 1|X|2称为哈代势。通过使用 Jeanjean 的单调性技巧,我们在非线性的一般 Berestycki-Lions 类型假设下承认上述问题的一类基态解G,以及一些关于潜力的弱假设 .

更新日期:2021-09-02
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