Multiplicity and concentration results for fractional Schrödinger‐Poisson systems involving a Bessel operator. (29th August 2018)

• Record Type: Journal Article
• Authors: Shen, Liejun
• Other Names: Aguiar Jesus Vigo guestEditor.; Rubio Raquel Garcia guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 17(2018)
• Page Start: 7599
• Page End: 7611
• Publication Date: 2018-08-29
• Subjects: Bessel operator -- concave‐convex -- concentration -- Mountain‐pass theorem -- multiplicity -- variational principle; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5223
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : This paper is concerned with the fractional Schrödinger‐Poisson systems involving a Bessel operator. By using Mountain‐pass theorem and Ekeland's variational principle, we obtain the multiplicity and concentration of nontrivial solutions for the given problem. In particular, although there exist concave‐convex nonlinearities in our problem, it is not necessary to assume that the corresponding Lebesgue norm of the weight function of the convex term needs to be small enough.