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The Existence of Global Solution for a Class of Semilinear Equations on Heisenberg Group

Zhujun Zheng·Keping Lu·Luo Xuebo
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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 $Z_2$ 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 $$ -Δ_{H^n} u=|u|^{p-1} u ~ x\in H^n $$ has infinite positive solutions. Our approach can also be applied to study more general nonlinear problems.

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Zhujun Zheng, Keping Lu, Luo Xuebo. 2002-01-17. The Existence of Global Solution for a Class of Semilinear Equations on Heisenberg Group. https://arxiv.org/abs/math/0201155

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