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Existence and nonexistence results for semilinear equations on the Heisenberg group. (English) Zbl 0793.35037
The aim of this paper is to establish existence, regularity and nonexistence results for the problem \[ \Delta_{\mathbb{H}^ n} u+f(u)=0 \quad \text{in } D,\qquad u |_{\partial D}=0, \] where \(D\) is an open (bounded or unbounded) subset of the Heisenberg group \(\mathbb{H}^ n\) and \(\Delta_{\mathbb{H}^ n}\) is the subelliptic Laplacian on \(\mathbb{H}^ n\).

MSC:
35J65 Nonlinear boundary value problems for linear elliptic equations
58J32 Boundary value problems on manifolds
58J10 Differential complexes
35D05 Existence of generalized solutions of PDE (MSC2000)
35D10 Regularity of generalized solutions of PDE (MSC2000)
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