Multiple solutions for quasi-linear elliptic equations with Berestycki-Lions type nonlinearity

被引：0
|
作者：
Wu, Maomao [1 ,2 ]
Liu, Haidong [2 ]
机构：
[1] Zhejiang Normal Univ, Sch Math Sci, Zhejiang 321004, Peoples R China
[2] Jiaxing Univ, Inst Math, Zhejiang 314001, Peoples R China
来源：
COMMUNICATIONS IN ANALYSIS AND MECHANICS | 2024年 / 16卷 / 02期
关键词：
nonhomogeneous quasi -linear elliptic equation; ground state solution; mountain pass type; solution; variational methods; SCALAR FIELD-EQUATIONS; SCHRODINGER-EQUATIONS; R-N; EXISTENCE;
D O I：
10.3934/cam.2024016
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We studied the modified nonlinear Schro<spacing diaeresis>dinger equation - Delta u - 1 2 Delta( u 2 ) u = g ( u ) + h ( x ) , u is an element of H 1 ( R N ) , (0.1) where N >= 3, g is an element of C ( R , R) is a nonlinear function of Berestycki-Lions type, and h t 0 is a nonnegative function. When II h II L 2 ( R N ) is suitably small, we proved that (0.1) possesses at least two positive solutions by variational approach, one of which is a ground state while the other is of mountain pass type.
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页码：334 / 344
页数：11
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