Weak solutions for a fractional equation in with Kirchhoff terms

Abstract

We explore the multiplicity of weak solutions to a nonlocal equation in governed by a fractional power of the p-Laplacian combined with a Kirchhoff-type term. The nonlinearity involves two real parameters, one of which is of perturbing nature, and can overpower the critical fractional exponent. Our arguments rely upon the variational apparatus; the lack of compactness of the Sobolev embeddings is circumvented by the use of convenient weight functions.

Keywords:

• Kirchhoff problem
• Schrödinger operator
• fractional p-Laplacian
• multiplicity

AMS Subject Classifications:

• 35J60
• 35R11

Acknowledgements

The authors are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

Notes

No potential conflict of interest was reported by the authors.

Because of a surprising coincidence of names within the same Department, we have to point out that the author was born on August 4, 1968.