An existence result for singular Finsler double phase problems

By Csaba Farkas, Patrick Winkert. Journal of Differential Equations, 2020

73 citations recorded by the source corpus.

In this paper, we study a class of singular double phase problems defined on Minkowski spaces in terms of Finsler manifolds and with right-hand sides that allow a certain type of critical growth for such problems. Under very general assumptions and based on variational tools we prove the existence of at least one nontrivial weak solution for such a problem. This is the first work dealing with a Finsler double phase operator even in the nonsingular case.

Subfields: Applied Mathematics, Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/7b1f80569f13e107a71f959790c542e378e95b85

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In Applied Mathematics

In Astronomy and Astrophysics

Citations in the corpus

New embedding results for double phase problems with variable exponents and a priori bounds for corresponding generalized double phase problems (2022, methodology): “We refer to the papers of BahrouniRădulescu-Winkert [3] (Baouendi-Grushin operator), Colasuonno-Squassina [15] (double phase eigenvalue problems), Farkas-Winkert [31] (Finsler double phase problems), Gasiński-Papageorgiou [32] (locally Lipschitz right-hand sides), Gasiński-Winkert [34, 35] (convecti”
On double phase Kirchhoff problems with singular nonlinearity (2021, methodology): “Further results in the context of double phase Kirchhoff problems can be found in the recent works of Arora et al. [1], Fiscella et al. [16], Gupta and Dwivedi [23], Ho and Winkert [25] and Isernia and Repovš [26].”
A new class of double phase variable exponent problems: Existence and uniqueness (2021, methodology): “For related works dealing with certain types of double phase problems we refer to the works of Barletta-Tornatore [5], BiagiEsposito-Vecchi [14], Farkas-Winkert [33], Liu-Winkert [49], Papageorgiou-Rădulescu-Repovš [56] and Rădulescu [60].”