New Existence of Solutions for the Fractional p-Laplacian Equations with Sign-Changing Potential and Nonlinearity

详细信息    查看全文

• 作者：Bitao Cheng ; Xianhua Tang
• 关键词：Mathematics Subject Classification35J20 ; 35J60
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：13
• 期：5
• 页码：3373-3387
• 全文大小：606 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1660-5454
• 卷排序：13

文摘

In the present paper, we consider the fractional p-Laplacian equation$$(-\Delta)_{p}^{s}u + V(x)|u|^{p-2}u = f(x, u),\quad \forall \in R^{N},$$ (1.1)where \({p \geq 2, N \geq 2}\), \({0 < s < 1}\), \({V \in C(R^N, R)}\) and \({f \in C(R^N \times R, R)}\) are allowed to be sign-changing. In such a double sign-changing case, a new result on the existence of nontrivial solutions for Eq. (1.1) is obtained via variational methods, which is even new for p =  2.Mathematics Subject Classification35J2035J60This work is partially supported by the NNFC (11571370, 11361048), YNEF (2014Z153) and YNSF (2013FD046).