We consider the following class of fractional problems with unbalanced growth: {(−Δ)psu+(−Δ)qsu+V(εx)(|u|p−2u+|u|q−2u)=f(u)in RN,u∈Ws,p(RN)∩Ws,q(RN),u>0in RN, where ε>0 is a small parameter, s∈(0,1), [Formula presented], (−Δ)ts (with t∈{p,q}) is the fractional t-Laplacian operator, V:RN→R is a continuous potential satisfying local conditions, and f:R→R is a continuous nonlinearity with subcritical growth. Applying suitable variational and topological arguments, we obtain multiple positive solutions for ε>0 sufficiently small as well as related concentration properties, in relationship with the set where the potential V attains its minimum.

Fractional double-phase patterns: concentration and multiplicity of solutions / Ambrosio, V.; Radulescu, V. D.. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - 142:(2020), pp. 101-145. [10.1016/j.matpur.2020.08.011]

Fractional double-phase patterns: concentration and multiplicity of solutions

Ambrosio V.;
2020-01-01

Abstract

We consider the following class of fractional problems with unbalanced growth: {(−Δ)psu+(−Δ)qsu+V(εx)(|u|p−2u+|u|q−2u)=f(u)in RN,u∈Ws,p(RN)∩Ws,q(RN),u>0in RN, where ε>0 is a small parameter, s∈(0,1), [Formula presented], (−Δ)ts (with t∈{p,q}) is the fractional t-Laplacian operator, V:RN→R is a continuous potential satisfying local conditions, and f:R→R is a continuous nonlinearity with subcritical growth. Applying suitable variational and topological arguments, we obtain multiple positive solutions for ε>0 sufficiently small as well as related concentration properties, in relationship with the set where the potential V attains its minimum.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/284884
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