Multiplicity and concentration of positive solutions for fractional nonlinear Schrodinger equations with critical growth
| dc.contributor.author | Shang, Xudong | |
| dc.contributor.author | Zhang, Jihui | |
| dc.date.accessioned | 2021-10-20T13:20:00Z | |
| dc.date.available | 2021-10-20T13:20:00Z | |
| dc.date.issued | 2019-02-12 | |
| dc.description.abstract | In this article we consider the multiplicity and concentration behavior of positive solutions for the fractional nonlinear Schrödinger equation ε2s (-Δ)su + V(x)u = u2*s-1 + ƒ(u), x ∈ ℝN, u ∈ Hs(ℝN), u(x) > 0, where ε is a positive parameter, s ∈ (0, 1), N > 2s and 2*s = 2N/N-2s is the fractional critical exponent, and ƒ is a C1 function satisfying suitable assumptions. We assume that the potential V(x) ∈ C(ℝN) satisfies infℝN V(x) > 0, and that there exits k points xj ∈ ℝN such that for each j = 1,..., k, V(xj) are strictly global minimum. By using the variational method, we show that there are at least k positive solutions for a small ε > 0. Moreover, we establish the concentration property of solutions as ε tends to zero. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 22 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Shang, X., & Zhang, J. (2019). Multiplicity and concentration of positive solutions for fractional nonlinear Schrodinger equations with critical growth. <i>Electronic Journal of Differential Equations, 2019</i>(24), pp. 1-22. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14675 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2019, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Fractional Schrödinger equations | |
| dc.subject | Multiplicity of solutions | |
| dc.subject | Critical growth | |
| dc.subject | Variational method | |
| dc.title | Multiplicity and concentration of positive solutions for fractional nonlinear Schrodinger equations with critical growth | |
| dc.type | Article |