p-Kirchhoff type problem with a general critical nonlinearity
Date
2018-04-11
Authors
Zhang, Huixing
Lin, Baiquan
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In 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.
Description
Keywords
p-Kirchhoff type problem, Critical growth, Variational methods
Citation
Zhang, 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.
Rights
Attribution 4.0 International