Author:
Zhang Yajing,Li Qiaoqin,Pang Lu
Abstract
We prove the existence of multiple positive solutions of fractional Laplace problems with critical growth, we consider the concave power case or the convex power case. We establish the relationship between the number of the local maximum points of the coefficient function of the critical nonlinearity and the number of the positive solutions of the equation For more information see https://ejde.math.txstate.edu/Volumes/2021/23/abstr.html
Reference31 articles.
1. A. Ambrosetti, H. Brezis, G. Cerami; Combined effects of concave and convex nonlinearities in some elliptic problems, J. Funct. Anal., 122 (1994), 519-543.
2. A. Ambrosetti, J. Garcia, I. Peral; Multiplicity reults for some nonlinear elliptic equations, J. Func. Anal., 137 (1996), 219-242.
3. J. H. Bae, Y. H. Kim; Multiple solutions for discontinuous elliptic problems involving the fractional Laplacian, Electron. J. Differential Equations, 2019 (18) (2019), 1-16.
4. A. Bahri, Y. Li; On a min-max procedure for the existence of a positive solution for certain scalar field equations in RN , Rev. Mat. Iberoam., 6 (1990), 1-15.
5. B. Barrios, E. Colorado, A. de Pablo, U. Sanchez; On some critical problems for the fractional Laplacian operator, J. Differ. Equ., 252 (2012), 6133-6162.