Existence of Entire Solutions for Quasilinear Equations in the Heisenberg Group
Keywords:
Heisenberg group, entire solutions, critical exponentsAbstract
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∗.
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