Fractional double-phase patterns: concentration and multiplicity of solutions

By Vincenzo Ambrosio, Vicentiu D. Rădulescu. 2020

99 citations recorded by the source corpus.

Abstract We consider the following class of fractional problems with unbalanced growth: { ( − Δ ) p s u + ( − Δ ) q s u + V ( e x ) ( | u | p − 2 u + | u | q − 2 u ) = f ( u ) in  R N , u ∈ W s , p ( R N ) ∩ W s , q ( R N ) , u > 0 in  R N , where e > 0 is a small parameter, s ∈ ( 0 , 1 ) , 2 ≤ p q N s , ( − Δ ) t s (with t ∈ { p , q } ) is the fractional t-Laplacian operator, V : R N → 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 e > 0 sufficiently small as well as related concentration properties, in relationship with the set where the potential V attains its minimum.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/caeb68a9b6d84cf5db3fd41d964aad090fc0d4f6

Citations in the corpus

• Growth conditions and regularity for weak solutions to nonlinear elliptic pdes (2020, unknown): “For related recent references we also quote Duzgun-Marcellini-Vespri [39], [40], Rǎdulescu-Zhang [63], [64], Cencelja-Rădulescu-Repovš [19], Papageorgiou-Rădulescu-Repovš-Dušan [62], Ambrosio-Rădulescu [1], Ragusa-Tachikawa [65], Chlebicka [20], Chlebicka-DeFilippis [21], [22], CupiniGiannetti-Giova”