A FRACTIONAL CRITICAL PROBLEM WITH SHIFTING SUBCRITICAL PERTURBATION

doi:10.1007/s10473-022-0317-3

Abstract

Abstract: In this paper, we consider a class of fractional problem with subcritical perturbation on a bounded domain as follows: \begin{equation*} (P_{k})\quad \left\{ \begin{array}{ll} \displaystyle (-\Delta)^s u=g(x)[(u-k)^+]^{q-1}+u^{2^{*}_{s}-1},\ \ &x\in \Omega,\\ \displaystyle u>0,\ \ &x\in \Omega,\\ \displaystyle u=0,\ \ &x\in \mathbb{R}^N\backslash \Omega. \end{array} \right. \end{equation*} We prove the existence of nontrivial solutions $u_{k}$ of $(P_{k})$ for each $k\in (0,\infty)$. We also investigate the concentration behavior of the solutions $u_{k}$ as $k\to \infty$.

Key words: Subcritical perturbation, nontrivial solutions, concentration

CLC Number:

35J20

Qi LI, Chang-Lin XIANG. A FRACTIONAL CRITICAL PROBLEM WITH SHIFTING SUBCRITICAL PERTURBATION[J].Acta mathematica scientia,Series B, 2022, 42(3): 1113-1124.

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