Blow-up of ground states of fractional Choquard equations

作者：Vilasi, Luca^*; Wang, Youjun

来源：Nonlinear Analysis, Theory, Methods and Applications, 2022, 225: 113117.

DOI：10.1016/j.na.2022.113117

• Choquard equation
• Fractional Laplacian
• Blow-up

We investigate the blow-up behavior of ground states of the fractional Choquard equation (-?)(s)u + u = (K-alpha * |u|(p epsilon))|u|(p epsilon-2)u in R-N, with s is an element of (0, 1), N > 4s, K-alpha Riesz potential of order alpha is an element of (0, N), as the exponent p(epsilon) approaches the upper critical growth regime in Hardy-Littlewood- Sobolev's inequality. We prove that the ground state u(epsilon) blows up in the sense that IIu(epsilon)II(L infinity(RN)) = o(epsilon(-N-2s/4s)) as epsilon -> 0(+).

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