Existence of multiple solutions and estimates of extremal values for a Kirchhoff type problem with fast increasing weight and critical nonlinearity
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Date
2018-07-17
Authors
Qian, Xiaotao
Chen, Jianqing
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we study the Kirchhoff type problem
-(α + ε ∫ℝ3 K(x)|∇u|2dx) div(K(x)∇u) = λK(x)ƒ(x)|u|q-2u + K(x)|u|4u,
where x ∈ ℝ3, 1 < q < 2, K(x) = exp(|x|α/4) with α ≥ 2, ε > 0 is small enough, and the parameters α, λ > 0. Under some assumptions on ƒ(x), we establish the existence of two nonnegative nontrivial solutions and obtain uniform lower estimates for extremal values of the problem via variational methods.
Description
Keywords
Variational methods, Kirchhoff type equation, Critical nonlinearity, Multiple solutions, Extremal values
Citation
Qian, X., & Chen, J. (2018). Existence of multiple solutions and estimates of extremal values for a Kirchhoff type problem with fast increasing weight and critical nonlinearity. <i>Electronic Journal of Differential Equations, 2018</i>(144), pp. 1-19.
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Attribution 4.0 International