Abstract
In this paper, we first prove the existence of solutions to Dirichlet problems involving the fractional g-Laplacian operator and lower order terms by appealing to sub- and supersolution methods. Moreover, we also state the existence of extremal solutions. Afterward, and under additional assumptions on the lower order structure, we establish by variational techniques the existence of multiple solutions: one positive, one negative and one with non-constant sign.
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Acknowledgements
A.S. and M.J.S.M are partially supported by ANPCyT under Grants PICT 2017-0704, PICT 2019-3837 and by Universidad Nacional de San Luis under Grants PROIPRO 03-2420. P. O. is supported by Proyecto Bienal B080 Tipo 1 (Res. 4142/2019-R). The authors thank the referee for her/his useful comments to improve the manuscript.
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Ochoa, P., Silva, A. & Marziani, M.J.S. Existence and multiplicity of solutions for a Dirichlet problem in fractional Orlicz–Sobolev spaces. Annali di Matematica 203, 21–47 (2024). https://doi.org/10.1007/s10231-023-01351-w
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DOI: https://doi.org/10.1007/s10231-023-01351-w