Existence results for critical growth Kohn-Laplace equations with jumping nonlinearities
Year: 2025
Type: article
Abstract: This article is concerned with the existence of nontrivial solutions to critical growth Kohn-Laplace equations with jumping nonlinearities. Or, more specifically, we consider the following Kohn-Laplace problem: − Δ H u = b u + − a u − + ∣ u ∣ Q ∗ − 2 u , in Ω , u = 0 , on ∂ Ω , \left\{\begin{array}{ll}-{\Delta }_{H}u=b{u}^{+}-a{u}^{-}+{| u| }^{{Q}^{\ast }-2}u,\hspace{1.0em}& {\rm{in}}\hspace{0.33em}\Omega ,\\ u=0,\hspace{1.0em}& {\rm{on}}\hspace{0.33em}\partial \Omega ,\end{array}\right. where Δ H {\Delta }_{H} is the Kohn-Laplacian on the Heisenberg group H n {{\mathbb{H}}}^{n} with n > 1 n\gt 1 , Q ∗ = 2 + 2 n {Q}^{\ast }=2+\frac{2}{n} is the critical Sobolev exponent for Δ H {\Delta }_{H} ,
Source: Demonstratio Mathematica
Authors: Yu-Cheng An, Guai-Qi Tian, Bi-Jun An
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,187
OpenAlex ID: W4412475101