Solutions of biharmonic equations with mixed nonlinearity

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• 作者：Bin Liu (1) (2)
  
  1. Geomathematics Key Laboratory of Sichuan Province ; Chengdu University of Technology ; Chengdu ; Sichuan ; 610059 ; P.R. China
  2. College of Geophysics ; Chengdu University of Technology ; Chengdu ; Sichuan ; 610059 ; P.R. China
  
• 关键词：35J35 ; 35J60 ; biharmonic equations ; mixed nonlinearity ; variational methods
• 刊名：Boundary Value Problems
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：2014
• 期：1
• 全文大小：1,195 KB
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• 刊物主题：Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations; Analysis; Approximations and Expansions; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1687-2770

文摘

In this paper, we study the following biharmonic equations with mixed nonlinearity: \(\Delta^{2}u-\Delta u+V(x)u=f(x, u)+\lambda\xi(x)|u|^{p-2}u\) , \(x\in{ \mathbb {R}}^{N}\) , \(u\in H^{2}({\mathbb {R}}^{N})\) , where \(V\in C(\mathbb{R}^{N})\) , \(\xi\in L^{\frac{2}{2-p}}(\mathbb {R}^{N})\) , \(1\leq p , and \(\lambda>0\) is a parameter. The existence of multiple solutions is obtained via variational methods. Some recent results are improved and extended.