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- Title
The sharp exponent in the study of the nonlocal Hénon equation in RN: a Liouville theorem and an existence result.
- Authors
Barrios, B.; Quaas, A.
- Abstract
We consider the nonlocal Hénon equation (- Δ) s u = | x | α u p , R N , where (- Δ) s is the fractional Laplacian operator with 0 < s < 1 , - 2 s < α , p > 1 and N > 2 s . We prove a nonexistence result for positive solutions in the optimal range of the nonlinearity, that is, when 1 < p < p α , s ∗ : = N + 2 α + 2 s N - 2 s. Moreover, we prove that a bubble solution, that is a fast decay positive radially symmetric solution, exists when p = p α , s ∗ .
- Subjects
EXISTENCE theorems; LIOUVILLE'S theorem; EQUATIONS; EXPONENTS
- Publication
Calculus of Variations & Partial Differential Equations, 2020, Vol 59, Issue 4, p1
- ISSN
0944-2669
- Publication type
Article
- DOI
10.1007/s00526-020-01763-z