Existence and uniqueness results for double phase problems with convection term

By Leszek Gasinski, Patrick Winkert. Journal of Differential Equations, 2019

185 citations recorded by the source corpus.

In this paper we consider quasilinear elliptic equations with double phase phenomena and a reaction term depending on the gradient. Under quite general assumptions on the convection term we prove the existence of a weak solution by applying the theory of pseudomonotone operators. Imposing some linear conditions on the gradient variable the uniqueness of the solution is obtained.

Subfields: Applied Mathematics, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/8e4a79daf2b33b972f9e392d1a01376243daf717

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In Applied Mathematics

In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

An existence result for singular Finsler double phase problems (2020, unknown): “We refer to the works of Bahrouni-Rădulescu-Winkert [1], Marino-Winkert [33], Papageorgiou-Rădulescu-Repovš [37], Papageorgiou-Winkert [39,40], Zeng-Bai-Gasiński-Winkert [48,47] and the references therein.”
Existence of solutions for double phase obstacle problems with multivalued convection term (2020, methodology): “which was recently studied by Gasiński-Winkert in [17].”
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”
A new class of double phase variable exponent problems: Existence and uniqueness (2021, background): “Other existence results for double phase problems based on truncation and comparison techniques can be found in the papers of Fiscella [34] (Hardy potentials), Fiscella-Pinamonti [35] (Kirchhoff type problem), Gasiński-Winkert [38, 39] (parametric and convection problems), Papageorgiou-Rădulescu-R”
Sign changing solution for a double phase problem with nonlinear boundary condition via the Nehari manifold (2020, methodology): “3) is different from the usual conditions when dealing with Dirichlet double phase problems, see, for example, [20] and [21] of the authors.”