Infinitely many solutions to a Kirchhoff-type equation involving logarithmic nonlinearity via Morse’s theory

In the present paper, we study the existence of infinitely many solutions for \(p(\textrm{x},\cdot )\) $p(\text{x},·)$ -fractional Kirchhoff-type elliptic equation involving logarithmic-type nonlinearities. Our approach is based on the computation of the critical groups in the nonlinear fractional elliptic problem of type \(p(\textrm{x},\cdot )\) $p(\text{x},·)$ -Kirchhoff, the Morse relation combined with variational methods.