Existence results for singular double phase problems by topological degree

Abdelaziz Sabiry, Ghizlane Zineddaine, Abderrazak Kassidi, Lalla Saadia Chadli

Abstract


In this paper we consider singular elliptic problems directed by the double phase operator, including a gradient-dependent reaction term as well as Dirichlet boundary conditions. Using topological degree methods for a class of non-continuous operators based on the abstract Hammerstein equation, we prove the existence of weak solutions in the Musielak-Orlicz-Sobolev space $W_0^{1,\mathcal{E}}(\mathfrak{O})$. Our assumptions are appropriate and different from those discussed above.

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DOI: https://doi.org/10.52846/ami.v52i1.1921