Multiple solutions for a p(x)-Kirchhoff-type equation with sign-changing nonlinearities

Abstract

Using the mountain pass theorem combined with the minimum principle, we obtain at least two non-negative, non-trivial weak solutions for a class of p(x)-Kirchhoff-type equations.

Keywords:

• p(x)-Kirchhoff-type equation
• sign-changing nonlinearities
• multiple solutions
• mountain pass theorem

AMS Subject Classifications::

• 34B27
• 35J60
• 35B05

Acknowledgements

The author would like to thank the referees for their suggestions and helpful comments which improved the presentation of the original manuscript. This work was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED).