Abstract
In this paper, we study the existence of weak solutions for a quasilinear elliptic system involving the fractional pseudo-differential (p(.), q(.))-Laplacian operators. The approach is based on mountain pass theorem in which we prove that the energy functional associated to our problem satisfies the Palais–Smale and two mountain pass geometric conditions.
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Boumazourh, A., Azroul, E. On a class of fractional systems with nonstandard growth conditions. J. Pseudo-Differ. Oper. Appl. 11, 805–820 (2020). https://doi.org/10.1007/s11868-019-00310-5
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DOI: https://doi.org/10.1007/s11868-019-00310-5
Keywords
- Elliptic systems
- Generalized fractional Sobolev spaces
- Variational methods
- Mountain pass theorem
- Fractional p(x)-Laplacian