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

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Qujing Normal University, 655011, Qujing, Yunnan, People’s Republic of China

    Bitao Cheng

  2. School of Mathematics and Statistics, Central South University, 410083, Changsha, Hunan, People’s Republic of China

    Xianhua Tang

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  1. Bitao Cheng
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  2. Xianhua Tang
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Correspondence to Bitao Cheng.

Additional information

This work is partially supported by the NNFC (11571370, 11361048), YNEF (2014Z153) and YNSF (2013FD046).

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Cheng, B., Tang, X. New Existence of Solutions for the Fractional p-Laplacian Equations with Sign-Changing Potential and Nonlinearity. Mediterr. J. Math. 13, 3373–3387 (2016). https://doi.org/10.1007/s00009-016-0691-y

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  • DOI: https://doi.org/10.1007/s00009-016-0691-y

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