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

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

2002-01-17

arxiv.org/abs/math/0201155v1

Mathematics

Analysis of PDEs

12 pages, 0 figures

Scientific paper

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 $$ -\Delta_{H^n} u=|u|^{p-1} u ~ x\in H^n $$ has infinite positive solutions. Our approach can also be applied to study more general nonlinear problems.

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