Zhang, HuixingLin, Baiquan2022-01-312022-01-312018-04-11Zhang, H., & Lin, B. (2018). p-Kirchhoff type problem with a general critical nonlinearity. <i>Electronic Journal of Differential Equations, 2018</i>(89), pp. 1-10.1072-6691https://hdl.handle.net/10877/15256In this article, we consider the p-Kirchhoff type problem (1 + λ ∫ℝN |∇u|p + λb ∫ℝN |u|p) (-∆pu + b|u|p-2u) = ƒ(u), x ∈ ℝN, where λ > 0, the nonlinearity ƒ can reach critical growth. Without the Ambrosetti-Robinowitz condition or the monotonicity condition on ƒ, we prove the existence of positive solutions for the p-Kirchhoff type problem. In addition, we also study the asymptotic behavior of the solutions with respect to the parameter λ → 0.Text10 pages1 file (.pdf)enAttribution 4.0 Internationalp-Kirchhoff type problemCritical growthVariational methodsArticle