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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:449

Article

He, Tieshan¹  Yao, Zheng-an²  Sun, Zhaohong¹ 

[1] Zhongkai Univ Agr & Engn, Sch Computat Sci, Guangzhou 5102259, Guangdong, Peoples R China

[2] Sun Yat Sen Univ, Sch Math & Computat Sci, Guangzhou 510275, Guangdong, Peoples R China

关键词: Nonhomogeneous differential operator;    Constant sign and nodal solutions;    Variational approach;    Gradient flow;    Truncation;    Critical growth;   

DOI  :  10.1016/j.jmaa.2016.12.020

来源: Elsevier

【 摘 要 】

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 lambda, 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 lambda 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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free