p-Laplacian equations in RN with finite potential via truncation method, the critical case

Abstract In this paper, we consider the problem − Δ p u + a ( x ) | u | p − 2 u = | u | p ⁎ − 2 u + μ | u | q − 2 u in R N , where 1 p N , max ⁡ { p , p ⁎ − 1 } q p ⁎ = N p N − p , μ > 0 , Δ p is the p-Laplacian operator, and the potential a ( x ) is positive and verifies suitable decay assumptions. We prove that the problem has infinitely many solutions by using truncation method.