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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 7 October 2019

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1570413619

Digital Object Identifier
doi:10.12775/TMNA.2019.078

Citation

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. https://projecteuclid.org/euclid.tmna/1570413619


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