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AbstractIn this paper, we consider the Dirichlet boundary value problem to singular semilinear subelliptic equation on the Heisenberg group −ΔHu=1uγ+f(u),γ>0.$$-\Delta_{\mathbb{H}}u=\frac{1}{u^{\gamma}}+f(u), \quad \gamma>0. $$ We prove the positivity and continuity up… Click to show full abstract
AbstractIn this paper, we consider the Dirichlet boundary value problem to singular semilinear subelliptic equation on the Heisenberg group −ΔHu=1uγ+f(u),γ>0.$$-\Delta_{\mathbb{H}}u=\frac{1}{u^{\gamma}}+f(u), \quad \gamma>0. $$ We prove the positivity and continuity up to the boundary for the weak solutions. We also conclude monotonicity of cylindrical solutions to the problem based on a study of the equation −ΔHu0=1u0γ$-\Delta_{\mathbb {H}}u_{0}=\frac{1}{u_{0}^{\gamma}}$. The main technique is a generalization of the moving plane method to the Heisenberg group.
Journal Title: Boundary Value Problems
Year Published: 2018
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