An existence result for singular Finsler double phase problems

On an anisotropic double phase problem with singular and sign changing nonlinearity

“…Although it is worth mentioning that anisotropic singular problem is very less understood. When a(x) = 0, singular anisotropic problems is studied in Biset-Mebrate-Mohammed [3], Farkas-Winkert [11] and Farkas-Fiscella-Winkert [10], Bal-Garain-Mukherjee [1]. To the best of our knowledge, in the double phase context, anisotropic singular problems has been first discussed in Farkas-Winkert [12], where the authors proved existence of one weak solution in the critical case.…”

Multiple solutions for nonlinear boundary value problems of Kirchhoff type on a double phase setting

“…Starting from [5], several authors studied existence and multiplicity results for nonlinear problems driven by (1.5), such as in [8,10,11,12,13,14,17,18,21,26] with the help of different variational techniques. In particular, in [14] Fiscella and Pinamonti provide existence and multiplicity results for Kirchhoff double phase problems but with Dirichlet boundary condition.…”

On double phase Kirchhoff problems with singular nonlinearity

“…Finally, we mention some existence and multiplicity results for double phase problems without Kirchhoff term, that is, m(t) ≡ 1 for all t ≥ 0. We refer to the papers of Arora-Shmarev [3,4] (parabolic double phase problems), Colasuonno-Squassina [10] (eigenvalue problems), Farkas-Winkert [18], Farkas-Fiscella-Winkert [17] (singular Finsler double phase problems), Fiscella [20] (Hardy potentials), Gasiński-Papageorgiou [26] (locally Lipschitz right-hand side), 28,29] (convection and superlinear problems), Liu-Dai [34] (Nehari manifold approach), Liu-Dai-Papageorgiou-Winkert [35] (singular problems), Perera-Squassina [43] (Morse theoretical approach), Zeng-Bai-Gasiński-Winkert [48,49] (multivalued obstacle problems) and the references therein.…”