We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Concentration behavior of ground state solutions for a fractional Schrödinger–Poisson system involving critical exponent.
- Authors
Yang, Zhipeng; Yu, Yuanyang; Zhao, Fukun
- Abstract
We are concerned with the existence and concentration behavior of ground state solutions of the fractional Schrödinger–Poisson system with critical nonlinearity 𝜀 2 s (− Δ) s u + V (x) u + ϕ u = λ | u | p − 2 u + | u | 2 s ∗ − 2 u in ℝ 3 , 𝜀 2 t (− Δ) t ϕ = u 2 in ℝ 3 , where 𝜀 > 0 is a small parameter, λ > 0 , 4 s + 2 t s + t < p < 2 s ∗ = 6 3 − 2 s , (− Δ) α denotes the fractional Laplacian of order α = s , t ∈ (0 , 1) and satisfies 2 t + 2 s > 3. The potential V is continuous and positive, and has a local minimum. We obtain a positive ground state solution for 𝜀 > 0 small, and we show that these ground state solutions concentrate around a local minimum of V as 𝜀 → 0.
- Subjects
CRITICAL exponents; POISSON'S equation; BEHAVIOR; CRITICAL point (Thermodynamics); MAXIMA &; minima
- Publication
Communications in Contemporary Mathematics, 2019, Vol 21, Issue 6, pN.PAG
- ISSN
0219-1997
- Publication type
Article
- DOI
10.1142/S021919971850027X