Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (3): 903-918.doi: 10.1007/s10473-022-0306-6

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ESTIMATES FOR EXTREMAL VALUES FOR A CRITICAL FRACTIONAL EQUATION WITH CONCAVE-CONVEX NONLINEARITIES

Jianghao HAO, Yajing ZHANG   

  1. School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, China
  • Received:2020-07-24 Published:2022-06-24
  • Contact: Yajing ZHANG,E-mail:zhangyj@sxu.edu.cn E-mail:zhangyj@sxu.edu.cn
  • Supported by:
    This work is partially supported by National Natural Science Foundation of China (11871315) and Natural Science Foundation of Shanxi Province of China (201901D111021)

Abstract: In this paper we study the critical fractional equation with a parameter λ and establish uniform lower bounds for Λ, which is the supremum of the set of λ, related to the existence of positive solutions of the critical fractional equation.

Key words: Multiple positive solutions, fractional Laplace problems, critical growth

CLC Number: 

  • 49J35
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