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Combined effects of singular and exponential nonlinearities in fractional Kirchhoff problems

  • * Corresponding author: Patrizia Pucci

    * Corresponding author: Patrizia Pucci 
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  • In this paper we establish the existence of at least two (weak) solutions for the following fractional Kirchhoff problem involving singular and exponential nonlinearities

    $ \begin{cases} M\left(\|u\|^{{n}/{s}}\right)(-\Delta)^s_{n/s}u = \mu u^{-q}+ u^{r-1}\exp( u^{\beta})\quad\text{in } \Omega,\\ u>0\qquad\text{in } \Omega,\\ u = 0\qquad\text{in } \mathbb R^n \setminus{ \Omega}, \end{cases} $

    where $ \Omega $ is a smooth bounded domain of $ \mathbb R^n $, $ n\geq 1 $, $ s\in (0,1) $, $ \mu>0 $ is a real parameter, $ \beta <{n/(n-s)} $ and $ q\in (0,1) $.The paper covers the so called degenerate Kirchhoff case andthe existence proofs rely on the Nehari manifold techniques.

    Mathematics Subject Classification: Primary: 35J60; Secondary: 35A15, 49J52.


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