On a -Kirchhoff equation via Krasnoselskii’s genus

In this work will use the genus theory, introduced by Krasnoselskii, to show a result of existence and multiplicity of solutions of the p -Kirchhoff equation − [ M ( ∫ Ω | ∇ u | p d x ) ] p − 1 Δ p u = f ( x , u ) in Ω , u = 0 on ∂ Ω where Ω is a bounded smooth domain of R N , 1 < p < N , and M and f are continuous functions.