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Quasilinear elliptic problems on non-reflexive Orlicz-Sobolev spaces

2019; Juliusz Schauder University Center for Nonlinear Studies; Linguagem: Inglês

10.12775/tmna.2019.078

1230-3429

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

Differential Equations and Boundary Problems

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.