Ground states and geometrically distinct solutions for periodic Choquard-Pekar equations

被引：61

作者：

Qin, Dongdong ^{[1
]}

Radulescu, Vicentiu D. ^{[2
,3
]}

Tang, Xianhua ^{[1
]}

机构：

[1] Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

[2] AGH Univ Sci & Technol, Fac Appl Math, Al Mickiewicza 30, PL-30059 Krakow, Poland

[3] Univ Craiova, Dept Math, St AI Cuza 13, Craiova 200585, Romania

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2021年 / 275卷

关键词：

Choquard-Pekar equation; Ground state solution; Strongly indefinite problem; Geometrically distinct solutions; SCHRODINGER-EQUATION; EXISTENCE;

D O I：

10.1016/j.jde.2020.11.021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the following non-autonomous Choquard-Pekar equation: {-Delta u + V(x)u = (W * F(u)) f(u), x is an element of R-N (N >= 2), u is an element of H-1 (R-N), where the potential V (x) is 1-periodic and 0 lies in a gap of the spectrum of the Schrodinger operator -Delta + V. Under some general assumptions on the potential W and the nonlinearity f , we show the existence of ground state solutions. We also construct infinitely many geometrically distinct solutions by using the variational method and deformation arguments. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：652 / 683

页数：32

共 48 条

[1] A Cauchy-Schwarz type inequality for bilinear integrals on positive measures [J].

Ackermann, N .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 133 (09) :2647-2656

[2] On a periodic Schrodinger equation with nonlocal superlinear part [J].

Ackermann, N .

MATHEMATISCHE ZEITSCHRIFT, 2004, 248 (02) :423-443

[3] LOCALIZED SOLUTIONS OF HARTREE-EQUATIONS FOR NARROW-BAND CRYSTALS [J].

ALBANESE, C .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1988, 120 (01) :97-103

[4]

Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7

[5]

[Anonymous], 1954, Untersuchung uiber die Elektronentheorie der Kristalle, DOI DOI 10.1515/9783112649305

[6]

[Anonymous], 1996, VARIATIONAL METHODS, DOI DOI 10.1007/978-3-662-03212-1

[7] Symmetry breaking regime in the nonlinear Hartree equation [J].

Aschbacher, WH ;

Fröhlich, J ;

Graf, GM ;

Schnee, K ;

Troyer, M .

JOURNAL OF MATHEMATICAL PHYSICS, 2002, 43 (08) :3879-3891

[8] Homoclinic solutions of an infinite-dimensional Hamiltonian system [J].

Bartsch, T ;

Ding, YH .

MATHEMATISCHE ZEITSCHRIFT, 2002, 240 (02) :289-310

[9] On a nonlinear Schrodinger equation with periodic potential [J].

Bartsch, T ;

Ding, YH .

MATHEMATISCHE ANNALEN, 1999, 313 (01) :15-37

[10] EXISTENCE OF A NONTRIVIAL SOLUTION TO A STRONGLY INDEFINITE SEMILINEAR EQUATION [J].

BUFFONI, B ;

JEANJEAN, L ;

STUART, CA .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 119 (01) :179-186

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