Critical fractional p-Laplacian problems with possibly vanishing potentials
Copyright policy )Critical fractional p-Laplacian problems with possibly vanishing potentials
We obtain nontrivial solutions of a critical fractional $p$-Laplacian equation in the whole space and with possibly vanishing potentials. In addition to the usual difficulty of the lack of compactness associated with problems involving critical Sobolev exponents, the problem is further complicated by the absence of a direct sum decomposition suitable for applying classical linking arguments. We overcome this difficulty using a generalized linking construction based on the ${\mathbb Z}_2$-cohomological index.
16 pages. arXiv admin note: text overlap with arXiv:1411.2198
- Catholic University of the Sacred Heart Italy
- Florida Institute of Technology United States
- Xiangnan University China (People's Republic of)
- University of Verona Italy
Vanishing potentials, critical exponent, external potentials, \(\mathbb{Z}_2\)-cohomological index, Existence problems for PDEs: global existence, local existence, non-existence, Fractional partial differential equations, Critical exponents in context of PDEs, nontrivial solutions, Mathematics - Analysis of PDEs, fractional p-Laplacian, vanishing potentials, existence of solution, fractional \(p\)-Laplacian, FOS: Mathematics, generalized linking, 35R11, 35B33, 58E05, fractional p-Laplacians, Quasilinear elliptic equations with \(p\)-Laplacian, Analysis of PDEs (math.AP)
Vanishing potentials, critical exponent, external potentials, \(\mathbb{Z}_2\)-cohomological index, Existence problems for PDEs: global existence, local existence, non-existence, Fractional partial differential equations, Critical exponents in context of PDEs, nontrivial solutions, Mathematics - Analysis of PDEs, fractional p-Laplacian, vanishing potentials, existence of solution, fractional \(p\)-Laplacian, FOS: Mathematics, generalized linking, 35R11, 35B33, 58E05, fractional p-Laplacians, Quasilinear elliptic equations with \(p\)-Laplacian, Analysis of PDEs (math.AP)
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).19 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!