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Licensed Unlicensed Requires Authentication Published online by De Gruyter February 1, 2024

Normalized solutions for the fractional Schrödinger equation with combined nonlinearities

  • Shengbing Deng EMAIL logo and Qiaoran Wu
From the journal Forum Mathematicum

Abstract

In this paper, we study the normalized solutions for the following fractional Schrödinger equation with combined nonlinearities

{ ( - Δ ) s u = λ u + μ | u | q - 2 u + | u | p - 2 u in  N , N u 2 𝑑 x = a 2 ,

where 0 < s < 1 , N > 2 s , 2 < q < p = 2 s * = 2 N N - 2 s , a , μ > 0 and λ is a Lagrange multiplier. Since the existence results for p < 2 s * have been proved, using an approximation method, that is, let p 2 s * , we obtain several existence results. Moreover, we analyze the asymptotic behavior of solutions as μ 0 and μ goes to its upper bound.

MSC 2020: 35R11; 35B33; 35J61

Communicated by Christopher D. Sogge


Award Identifier / Grant number: 12371121

Funding statement: The authors were supported by National Natural Science Foundation of China, Grant No. 12371121.

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Received: 2023-11-22
Published Online: 2024-02-01

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