Existence and Concentration of Semiclassical Bound States for a Quasilinear Schrodinger-Poisson System

被引：0
|
作者：
Ramos, Gustavo de Paula [1 ]
Siciliano, Gaetano [2 ]
机构：
[1] Univ Sao Paulo, Dept Matemat, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, SP, Brazil
[2] Univ Bari Aldo Moro, Dept Matemat, via E Orabona 4, I-70126 Bari, Italy
来源：
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2024年 / 47卷 / 06期
基金：
巴西圣保罗研究基金会;
关键词：
Quasilinear Schrodinger-Poisson equations; Perturbation methods; Nonlocal problems; Semiclassical states; Asymptotic behavior; ASYMPTOTIC-BEHAVIOR; EQUATIONS;
D O I：
10.1007/s40840-024-01761-w
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In the paper we consider the following quasilinear Schrodinger-Poisson system in the whole space R-3 {-epsilon(2) Delta u + (V + phi)u = u |u|(p-1) {- Delta phi - beta Delta(4)phi = u(2), where 1 < p < 5, beta > 0, V : R-3 ->]0, infinity[ , and look for solutions u, phi : R-3 -> R in the semiclassical regime, namely when epsilon -> 0. By means of the Lyapunov-Schmidt method we estimate the number of solutions by the cup-length of the critical manifold of the external potential V.
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页数：26
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