Infinitely many solutions for fractional Kirchhoff–Sobolev–Hardy critical problems

Abstract

We investigate a class of critical stationary Kirchhoff fractional $p$-Laplacian problems in presence of a Hardy potential. By using a suitable version of the symmetric mountain-pass lemma due to Kajikiya, we obtain the existence of a sequence of infinitely many arbitrarily small solutions converging to zero.

Keywords

• fractional $p$-laplacian
• kirchhoff coefficient
• hardy potentials
• critical sobolev exponent
• variational methods