Topological Methods in Nonlinear Analysis

Quasilinear elliptic problems on non-reflexive Orlicz-Sobolev spaces

Edcarlos D. Silva, Marcos L. M. Carvalho, Kaye Silva, and José V. Gonçalves

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In the paper the existence, uniqueness and the multiplicity of solutions for a quasilinear elliptic problems driven by the $\Phi$-Laplacian operator is established. Here we consider the non-reflexive case taking into account the Orlicz and Orlicz-Sobolev framework. The non-reflexive case occurs when the $N$-function $\widetilde{\Phi}$ does not verify the $\Delta_{2}$-condition. In order to prove our main results we employ variational methods, regularity results and truncation arguments.

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Topol. Methods Nonlinear Anal., Advance publication (2019), 26 pp.

First available in Project Euclid: 7 October 2019

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Silva, Edcarlos D.; Carvalho, Marcos L. M.; Silva, Kaye; Gonçalves, José V. Quasilinear elliptic problems on non-reflexive Orlicz-Sobolev spaces. Topol. Methods Nonlinear Anal., advance publication, 7 October 2019. doi:10.12775/TMNA.2019.078.

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