Name
Title | ||
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On the fractional Schrödinger-Kirchhoff equations with electromagnetic fields and critical nonlinearity. |
Abstract | ||
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Abstract In this paper, we consider the fractional Schrodinger–Kirchhoff equations with electromagnetic fields and critical nonlinearity e 2 s M ( [ u ] s , A e 2 ) ( − Δ ) A e s u + V ( x ) u = | u | 2 s ∗ − 2 u + h ( x , | u | 2 ) u , x ∈ R N , u ( x ) → 0 , as | x | → ∞ , where ( − Δ ) A e s is the fractional magnetic operator with 0 s 1 , 2 s ∗ = 2 N ∕ ( N − 2 s ) , M : R 0 + → R + is a continuous nondecreasing function, V : R N → R 0 + and A : R N → R N are the electric and magnetic potentials, respectively. By using the fractional version of the concentration compactness principle and variational methods, we show that the above problem: (i) has at least one solution provided that e E ; and (ii) for any m ∗ ∈ N , has m ∗ pairs of solutions if e E m ∗ , where E and E m ∗ are sufficiently small positive numbers. Moreover, these solutions u e → 0 as e → 0 . |
Year | Venue | DocType |
|---|---|---|
2018 | Computers & Mathematics with Applications | Journal |
Volume | Issue | Citations |
75 | 5 | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sihua Liang | 1 | 0 | 0.34 |
| Dusan Repovš | 2 | 21 | 11.09 |
| Binlin Zhang | 3 | 0 | 1.69 |