LEAST ACTION NODAL SOLUTIONS FOR THE QUADRATIC CHOQUARD EQUATION

被引：56

作者：

Ghimenti, Marco ^{[1
]}

Moroz, Vitaly ^{[2
]}

Van Schaftingen, Jean ^{[3
]}

机构：

[1] Univ Pisa, Dipartimento Matemat, Largo B Pontecorvo 5, I-56100 Pisa, Italy

[2] Swansea Univ, Dept Math, Singleton Pk, Swansea SA2 8PP, W Glam, Wales

[3] Catholic Univ Louvain, Inst Rech Math & Phys, Chemin Cyclotron 2 Bte L7-01-01, B-1348 Louvain La Neuve, Belgium

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2017年 / 145卷 / 02期

关键词：

Stationary nonlinear Schrodinger-Newton equation; stationary Hartree equation; nodal Nehari set; concentration; compactness; CONCENTRATION-COMPACTNESS PRINCIPLE; GROUND-STATES; EXISTENCE; CALCULUS;

D O I：

10.1090/proc/13247

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the existence of a minimal action nodal solution for the quadratic Choquard equation -Delta u + u = (I-alpha * parallel to u parallel to(2))u in R-N, where I-alpha is the Riesz potential of order alpha is an element of (0, N). The solution is constructed as the limit of minimal action nodal solutions for the nonlinear Choquard equations -Delta u + u = (I-alpha * parallel to u parallel to(p))vertical bar u vertical bar(p-2) u in R-N, when p -> 2. The existence of minimal action nodal solutions for p > 2 can be proved using a variational minimax procedure over a Nehari nodal set. No minimal action nodal solutions exist when p < 2.

引用

页码：737 / 747

页数：11

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