Multiplicity and concentration of positive solutions to the fractional Kirchhoff type problems involving sign-changing weight functions

Jie Yang; Haibo Chen

doi:10.3934/cpaa.2021096

Article Contents

2021, Volume 20, Issue 9: 3065-3092. Doi: 10.3934/cpaa.2021096

This issue Previous Article On the hot spots of quantum graphs Next Article On the stability of boundary equilibria in Filippov systems

Multiplicity and concentration of positive solutions to the fractional Kirchhoff type problems involving sign-changing weight functions

Jie Yang^1,2, and
Haibo Chen^1, ,

1.
School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, 410083, China
2.
School of Mathematics and Computational Science, Huaihua University, Huaihua, 418008, China

^* Corresponding author
^* Corresponding author

Received: November 2020

Revised: May 2021

Early access: June 2021

Published: September 2021

This work was supported by the National Natural Science Foundation of China (No. 12071486), the Research Foundation of Education Bureau of Hunan Province, China (No. 20B457, 19B450, 20A387)

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Abstract

The aim of this paper is to study the multiplicity and concentration of positive solutions to the fractional Kirchhoff type problems involving sign-changing weight functions and concave-convex nonlinearities with subcritical or critical growth. Applying Nehari manifold, fibering maps and Ljusternik-Schnirelmann theory, we investigate a relationship between the number of positive solutions and the topology of the global maximum set of $ K $.

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Mathematics Subject Classification: Primary: 35A11, 35B33; Secondary: 35R11.

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