Multiple and nodal solutions for parametric Neumann problems with nonhomogeneous differential operator and critical growth

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• 作者：Tieshan He^a ; ^{hetieshan68@163.com} ; Zheng-an Yao^b ; Zhaohong Sun^a
• 关键词：Nonhomogeneous differential operator ; Constant sign and nodal solutions ; Variational approach ; Gradient flow ; Truncation ; Critical growth
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 May 2017
• 年：2017
• 卷：449
• 期：2
• 页码：1133-1151
• 全文大小：464 K
• 卷排序：449

文摘

We consider a parametric Neumann problem with nonhomogeneous differential operator and critical growth. Combining variational methods based on critical point theory, with suitable truncation techniques and flow invariance arguments, we show that for all large λ, the problem has at least three nontrivial smooth solutions, two of constant sign (one positive, the other negative) and the third nodal. We also study the asymptotic behavior of all solutions obtained when λ converges to infinity. The interesting point is that we do not impose any restrictions to the behavior of the nonlinear term f at infinity. Our work unifies and sharply improves several recent papers.