Sign changing solution for a double phase problem with nonlinear boundary condition via the Nehari manifold

By Leszek Gasinski, Patrick Winkert. Journal of Differential Equations, 2020

101 citations recorded by the source corpus.

In this paper we study quasilinear elliptic equations driven by the so-called double phase operator and with a nonlinear boundary condition. Due to the lack of regularity, we prove the existence of multiple solutions by applying the Nehari manifold method along with truncation and comparison techniques and critical point theory. In addition, we can also determine the sign of the solutions (one positive, one negative, one nodal). Moreover, as a result of independent interest, we prove for a general class of such problems the boundedness of weak solutions.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/b7fce8ce967d12679ff0af6df83202b8f675fb67

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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 also mention the boundedness results in the works of Barletta-Cianchi-Marino [4] (for problems in Orlicz spaces), Gasiński-Winkert [33, 35] (for double phase Dirichlet and Neumann problems), Ho-Sim [40] (for weighted problems), Kim-Kim-Oh-Zeng [44] (for variable exponent double phase problems wit”
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, methodology): “Multiplicity results including sign-changing solutions have been obtained by Gasiński-Papageorgiou [37], Liu-Dai [48] and Gasiński-Winkert [40] via the Nehari manifold treatment due to the lack of regularity results for such problems.”