Existence and multiplicity of solutions for a superlinear Kirchhoff-type equations with critical Sobolev exponent in

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• 作者：Hong-Ying Li^a ; Jia-Feng Liao^a ; ^b ; ^{liaojiafeng@163.com}
• 关键词：Kirchhoff-type equation ; Critical exponent ; Positive solutions ; Infinitely many solutions ; Variational method
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：72
• 期：12
• 页码：2900-2907
• 全文大小：400 K
• 卷排序：72

文摘

In this article, we consider a class of superlinear Kirchhoff-type equations with critical growth {−(a+b∫RN∣∇u∣2dx)Δu=μu2∗−1+λk(x)uq−1,x∈RN,u∈D1,2(RN), where λ,μ>0,N≥4,2≤q<2∗,2∗=2NN−2,a,b≥0 and a+b>0a+b>0,kk satisfies some conditions. By using the variational method, the multiplicity of positive solutions and infinitely many pairs of solutions are obtained.