Advances in Differential Equations

Ground and bound state solutions for a Schrödinger system with linear and nonlinear couplings in $\mathbb{R}^N$

Kanishka Perera, Cyril Tintarev, Jun Wang, and Zhitao Zhang

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Abstract

We study the existence of ground and bound state solutions for a system of coupled Schrödinger equations with linear and nonlinear couplings in $\mathbb{R}^N$. By studying the limit system and using concentration compactness arguments, we prove the existence of ground and bound state solutions under suitable assumptions. Our results are new even for the limit system.

Article information

Source
Adv. Differential Equations, Volume 23, Number 7/8 (2018), 615-648.

Dates
First available in Project Euclid: 11 May 2018

Permanent link to this document
https://projecteuclid.org/euclid.ade/1526004068

Mathematical Reviews number (MathSciNet)
MR3801833

Zentralblatt MATH identifier
06889039

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 35J61: Semilinear elliptic equations 35J20: Variational methods for second-order elliptic equations 35Q60: PDEs in connection with optics and electromagnetic theory 49J40: Variational methods including variational inequalities [See also 47J20]

Citation

Perera, Kanishka; Tintarev, Cyril; Wang, Jun; Zhang, Zhitao. Ground and bound state solutions for a Schrödinger system with linear and nonlinear couplings in $\mathbb{R}^N$. Adv. Differential Equations 23 (2018), no. 7/8, 615--648. https://projecteuclid.org/euclid.ade/1526004068


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