Existence and concentration of ground state solutions for a critical nonlocal Schrödinger equation in R2

By Claudianor Oliveira Alves, Daniele Cassani, Cristina Tarsi, Minbo Yang. 2016

150 citations recorded by the source corpus.

We study the following singularly perturbed nonlocal Schrodinger equation −e2Δu+V(x)u=eμ−2[1|x|μ⁎F(u)]f(u)inR2, where V(x) is a continuous real function on R2, F(s) is the primitive of f(s), 0<μ<2 and e is a positive parameter. Assuming that the nonlinearity f(s) has critical exponential growth in the sense of Trudinger–Moser, we establish the existence and concentration of solutions by variational methods.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/a2c02dca7dd162ccc4e0c0689df639d1aad78f2c

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In Applied Mathematics

1. Fashun Gao
2. Minbo Yang
3. Marco Squassina
4. Claudianor Oliveira Alves
5. Jianjun Zhang
6. Daniele Cassani
7. Giovany M. Figueiredo
8. Vicentiu D. Rădulescu

In Computational Theory and Mathematics

1. Minbo Yang
2. Fashun Gao
3. Marco Squassina
4. Claudianor Oliveira Alves
5. Jianjun Zhang
6. Daniele Cassani
7. Giovany M. Figueiredo
8. Patrick Winkert

In Numerical Analysis

1. Minbo Yang
2. Marco Squassina
3. Claudianor Oliveira Alves
4. Jianjun Zhang
5. Daniele Cassani

Citations in the corpus

• The Brezis-Nirenberg type critical problem for the nonlinear Choquard equation (2016, background): “In [2], the authors studied the existence and concentrations of the solutions of a nonlocal Schrödinger with the critical exponential growth in R(2), that problem is closely related to the Choquard equation.”
• On nonlocal Choquard equations with Hardy-Littlewood-Sobolev critical exponents (2016, background): “To the best knowledge of the authors, there are not so many papers considering the Choquard equation with critical growth, for problem set on R(2) the second author and his collaborators in [2] considered the case of critical growth in the sense of Trudinger-Moser inequality and studied the existenc”
• Singularly perturbed critical Choquard equations (2016, background): “The planar case was considered by [3], where the authors first established the existence of ground state for the limit problem with critical exponential growth and then studied the concentration around the global minimum set.”