We investigate the existence and the multiplicity of solutions of the problem (Formula presented.) where Ω is a smooth, bounded domain of (Formula presented.), 1 < p < q < ∞, and the nonlinearity g behaves as uq − 1 at infinity. We use variational methods and find multiple solutions as minimax critical points of the associated energy functional. Under suitable assumptions on the nonlinearity, we cover also the resonant case.
Multiple solutions for asymptotically q-linear (p, q)-Laplacian problems
Colasuonno F.
2022-01-01
Abstract
We investigate the existence and the multiplicity of solutions of the problem (Formula presented.) where Ω is a smooth, bounded domain of (Formula presented.), 1 < p < q < ∞, and the nonlinearity g behaves as uq − 1 at infinity. We use variational methods and find multiple solutions as minimax critical points of the associated energy functional. Under suitable assumptions on the nonlinearity, we cover also the resonant case.
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