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 genera...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 -ΔH^nu=|u|^p-1u,x∈H^n has infinite positive solutions. Our approach can also be applied to study more general nonlinear problems.展开更多
文摘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 -ΔH^nu=|u|^p-1u,x∈H^n has infinite positive solutions. Our approach can also be applied to study more general nonlinear problems.
