Nonlocal p-Kirchhoff equations with singular and critical nonlinearity terms.

The objective of this work is to investigate a nonlocal problem involving singular and critical nonlinearities: ([ u ] s , p p) σ − 1 (− Δ) p s u = λ u γ + u p s ∗ − 1 in Ω , u > 0 , in Ω , u = 0 , in R N ∖ Ω , where Ω is a bounded domain in R N with the smooth boundary ∂ Ω , 0 < s < 1 < p < ∞ , N > s p , 1 < σ < p s ∗ / p , with p s ∗ = N p N − p s , (− Δ) p s is the nonlocal p-Laplace operator and [ u ] s , p is the Gagliardo p-seminorm. We combine some variational techniques with a truncation argument in order to show the existence and the multiplicity of positive solutions to the above problem. [ABSTRACT FROM AUTHOR]