On fractional Laplacian problems with indefinite nonlinearity

Abstract

In this paper, we study the existence of positive solutions for the following Laplacian problem with indefinite nonlinearity

where is a bounded domain and a(x) is a sign-changing function. For suitable conditions on a(x) and p, we prove: there exists such that problem has a positive solution for and has no positive solution for , where is the first eigenvalue of the fractional Laplacian operator.

Keywords:

• Fractional Laplacian operator
• positive solution
• indefinite nonlinearity

AMS Subject Classifications:

• 35R11
• 35A01
• 35A15

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11371110], [grant number 11601103].