We deal with the following nonlinear problem involving fractional p&q Laplacians: (−∆)spu + (−∆)squ + |u|p−2u + |u|q−2u = λh(x)f(u) + |u|qs∗−2u in RN, where s ∈ (0, 1), 1 < p < q < Ns , qs∗ = NNq−sq, λ > 0 is a parameter, h is a nontrivial bounded perturbation and f is a superlinear continuous function with subcritical growth. Using suitable variational arguments and concentration-compactness lemma, we prove the existence of a nontrivial non-negative solution for λ sufficiently large.
Fractional p&q Laplacian problems in RN with critical growth
Ambrosio V.
2020-01-01
Abstract
We deal with the following nonlinear problem involving fractional p&q Laplacians: (−∆)spu + (−∆)squ + |u|p−2u + |u|q−2u = λh(x)f(u) + |u|qs∗−2u in RN, where s ∈ (0, 1), 1 < p < q < Ns , qs∗ = NNq−sq, λ > 0 is a parameter, h is a nontrivial bounded perturbation and f is a superlinear continuous function with subcritical growth. Using suitable variational arguments and concentration-compactness lemma, we prove the existence of a nontrivial non-negative solution for λ sufficiently large.File in questo prodotto:
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