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.. - In: ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN. - ISSN 0232-2064. - 39:3(2020), pp. 289-314. [10.4171/ZAA/1661]
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
