On the fractional P – Q laplace operator with weights

AbstractWe exploit the existence and non-existence of positive solutions to the eigenvalue problem driven by the nonhomogeneous fractional p1(2):45–121]. to overcome the difficulty. Our paper can be considered as a counterpart to the important works Alves et al. Existence, multiplicity and concentration for a class of fractional p18(4):2009–2045, Benci et al. An eigenvalue problem for a quasilinear elliptic field equation. J Differ Equ, 2002;184(2):299–320, Bobkov et al. On positive solutions for (p,q)-Laplace equations with two parameters, Calc Var Partial Differ Equ, 2015;54(3):3277–3301, Colasuonno and Squassina. Eigenvalues for double phase variational integrals, Ann Mat Pura Appl (4), 2016;195(6):1917–1956, Papageorgiou et al. Positive solutions for nonlinear Neumann problems with singular terms and convection, J Math Pures Appl (9), 2020;136:1–21, Papageorgiou et al. Ground state and nodal solutions for a class of double phase problems, Z Angew Math Phys, 2020;71:1–15, and may have further applications to deal with other problems.Keywords: Fractional p–q laplacianvariational methodsmountain pass theoremAMS Classifications: 35J7035J6235B5035B51 AcknowledgementsWe would like to express our sincere thanks to the reviewer for their careful reading of the original manuscript and their helpful suggestions. We also deeply thank the editors for their correspondence.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe first author was supported by National key program for the development of Mathematics in the period from 2021 to 2030 (Grant B2024-CTT-01).