Existence of positive solutions to -Kirchhoff-type problem without compactness conditions

In this paper, we study the existence of positive solutions to p -Kirchhoff-type problem (0.1) { ( a + λ ( ∫ R N ( | ∇ u | p + b | u | p ) d x ) τ ) ( − Δ p u + b | u | p − 2 u ) = | u | m − 2 u + μ | u | q − 2 u , x ∈ R N u ( x ) > 0 , x ∈ R N , u ( x ) ∈ W 1 , p ( R N ) , where a , b > 0 , τ , λ ≥ 0 , μ ∈ R , 1 < p < N , p < q < m < p ∗ = p N N − p . A new existence result for (0.1) is obtained by the Nehari manifold method. This result can be regarded as an extension of the result in Li et al. (2012).