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Quasilinear elliptic problems with concave–convex nonlinearities

2016; World Scientific; Volume: 19; Issue: 06 Linguagem: Inglês

10.1142/s0219199716500504

1793-6683

Marcos L. M. Carvalho, Edcarlos D. da Silva, C. Goulart,

Numerical methods in inverse problems

In this paper, the existence and multiplicity of solutions for a quasilinear elliptic problem driven by the [Formula: see text]-Laplacian operator is established. These solutions are also built as ground state solutions using the Nehari method. The main difficulty arises from the fact that the [Formula: see text]-Laplacian operator is not homogeneous and the nonlinear term is indefinite.