Geodesic
Existence of entire solutions for quasilinear equations in the Heisenberg group
Minimax theory and its applications, Tome 4 (2019) no. 1
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The paper deals with the existence of entire solutions for a quasilinear equation ( λ) in Hn, depending on a real parameter λ, which involves a general elliptic operator A in divergence form and two main nonlinearities. The competing nonlinear terms combine each other. Under some conditions, we prove the existence of a critical value λ∗ > 0 with the property that ( λ) admits nontrivial nonnegative entire solutions if and only if λ λ∗. Furthermore, under the further assumption that the potential A of A is uniform convex, we give the existence of a second independent nontrivial nonnegative entire solution of ( λ), when λ > λ∗.
Mots-clés : Heisenberg group, entire solutions, critical exponents 
@article{MTA_2019_4_1_a9,
     author = {Patrizia Pucci},
     title = {Existence of entire solutions for quasilinear equations in the {Heisenberg} group},
     journal = {Minimax theory and its applications},
     year = {2019},
     volume = {4},
     number = {1},
     zbl = {1432.35090},
     url = {http://geodesic.mathdoc.fr/item/MTA_2019_4_1_a9/}
}
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Patrizia Pucci. Existence of entire solutions for quasilinear equations in the Heisenberg group. Minimax theory and its applications, Tome 4 (2019) no. 1. http://geodesic.mathdoc.fr/item/MTA_2019_4_1_a9/