Positive solutions for fractional Laplacian system involving concave-convex nonlinearities and sign-changing weight functions



	Positive solutions for fractional Laplacian system involving concave-convex nonlinearities and sign-changing weight functions


	Fixed Point Theory, Volume 22, No. 1, 2021, 407-430, February 1st, 2021 DOI: 10.24193/fpt-ro.2021.1.28 Authors: Maoding Zhen Abstract: In this paper, we consider a fractional Laplacian system with both concave-convex nonlinearities and sign-changing weight functions in bounded domains. With the help of the Nehari manifold, we prove that the system has at least two positive solutions when the pair of the parameters (λ,μ) belongs to a certain subset of ℝⁿ. Key Words and Phrases: Fractional Laplacian, critical exponent, subcritical exponent, ground state solution, fixed point. 2010 Mathematics Subject Classification: 35J50, 35B33, 35R11, 47H10. Published on-line: February 1st, 2021. Abstract pdf Fulltext pdf Back to volume's table of contents