Singularly perturbed critical Choquard equations
By Claudianor Oliveira Alves, Fashun Gao, Marco Squassina, Minbo Yang. 2016
180 citations recorded by the source corpus.
Abstract In this paper we study the semiclassical limit for the singularly perturbed Choquard equation − e 2 Δ u + V ( x ) u = e μ − 3 ( ∫ R 3 Q ( y ) G ( u ( y ) ) | x − y | μ d y ) Q ( x ) g ( u ) in R 3 , where 0 μ 3 , e is a positive parameter, V , Q are two continuous real function on R 3 and G is the primitive of g which is of critical growth due to the Hardy–Littlewood–Sobolev inequality. Under suitable assumptions on g, we first establish the existence of ground states for the critical Choquard equation with constant coefficients. Next we establish existence and multiplicity of semi-classical solutions and characterize the concentration behavior by variational methods.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/351a6379381e0ba79cedca708a6408f1e936253e
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In Applied Mathematics
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Citations in the corpus
- Existence and non-existence results for Kirchhoff-type problems with convolution nonlinearity (2018, unknown): “Therefore, there exists û ∈ H1(R3) \ {0} such that, passing to a subsequence, {{{ {{{ { ûn ⇀ û in H1(R3), ûn ⇀ û in Ls loc(R 3) for all s ∈ [1, 6), ûn → û, a.”
- Choquard-type equations with Hardy–Littlewood–Sobolev upper-critical growth (2018, methodology): “Here we borrow some ideas from [4, 45] to establish boundedness, decay, positivity and symmetry of ground state solutions to (1.”