The Existence of Global Solution for a Class of Semilinear Equations on Heisenberg Group
Zhujun Zheng, Keping Lu, Luo Xuebo
Abstract
Based on the concepts of a generalized critical point and the corresponding generalized P.S. condition introduced by Duong Minh Duc[1], we have proved a new Z2 index theorem and get a result on multiplicity of generalized critical points. Using the result and a quite standard variational method, it is found that the equation -ΔHn u=|u|p-1 u ~ x∈ Hn has infinite positive solutions. Our approach can also be applied to study more general nonlinear problems.
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