Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
839404 | Nonlinear Analysis: Theory, Methods & Applications | 2016 | 13 Pages |
Abstract
A higher order Kirchhoff type equation ∫R2m(∣∇mu∣2+∑γ=0m−1aγ(x)∣∇γu∣2)dx((−Δ)mu+∑γ=0m−1(−1)γ∇γ⋅(aγ(x)∇γu))=f(x,u)∣x∣β+ϵh(x)in R2m is considered in this paper. We assume that the nonlinearity of the equation has exponential critical growth and prove that, for a positive ϵϵ which is small enough, there are two distinct nontrivial solutions to the equation. When ϵ=0ϵ=0, we also prove that the equation has a nontrivial mountain-pass type solution.
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Authors
Liang Zhao, Ning Zhang,