Abstract.
We consider the quasilinear system
where \(\varepsilon > 0, 2 \leq p < N\), V and W are positive continuous potentials, Q is an homogeneous function with subcritical growth, \(H(u, v) = |u|^{\alpha}|v|^{\beta}\) with \(\alpha,\beta \geq 1\) satisfying \(\alpha + \beta = Np/(N - p)\). We relate the number of solutions with the topology of the set where V and W attain it minimum values. We consider the subcritical case γ = 0 and the critical case γ = 1. In the proofs we apply Ljusternik-Schnirelmann theory.
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The second author was partially supported by FEMAT-DF
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Figueiredo, G.M., Furtado, M.F. Multiple positive solutions for a quasilinear system of Schrödinger equations. Nonlinear differ. equ. appl. 15, 309–334 (2008). https://doi.org/10.1007/s00030-008-7051-y
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DOI: https://doi.org/10.1007/s00030-008-7051-y