Constant sign solutions for double phase problems with superlinear nonlinearity
By Leszek Gasinski, Patrick Winkert. Nonlinear Analysis, 2019
113 citations recorded by the source corpus.
We study parametric double phase problems involving superlinear nonlinearities without supposing any growth condition. Based on truncation and comparison methods the existence of two constant sign solutions is shown provided the parameter is larger than the first eigenvalue of the $p$-Laplacian. As a result of independent interest we prove a priori estimates for solutions for a general class of double phase problems with convection term.
View Paper: https://www.semanticscholar.org/paper/1614823b55cef441d6021d4e892ba50d64466aab
How researchers see this paper
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- Patrick Winkert
- Ángel Crespo-Blanco
- Leszek Gasinski
- Shengda Zeng
- Petteri Harjulehto
- Ky Ho
- Yunru Bai
- Nikolaos S. Papageorgiou
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.”
- 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.”
- Existence of solutions for double phase obstacle problems with multivalued convection term (2020, background): “In addition, when f is a single-valued function, the above problem reduces to − div ( |∇u|p−2∇u + μ(x)|∇u|q−2∇u ) = f(x, u,∇u) in Ω, u = 0 on ∂Ω, (1.2) which was recently studied by Gasiński-Winkert in [17].”