This paper deals with the standing wave for a Hamiltonian nonlinear wave equation which can be viewed as a representative of the class of equations of interest.On the one hand,by proving a compactness lemma and solvin...This paper deals with the standing wave for a Hamiltonian nonlinear wave equation which can be viewed as a representative of the class of equations of interest.On the one hand,by proving a compactness lemma and solving a variational problem,the existence of the standing wave with ground state for the aforementioned equation is proved.On the other hand,the authors derive the instability of the standing wave by applying the potential well argument,the concavity method and an invariant region under the solution flow of the Cauchy problem for the equation under study,and the invariance of the region aforementioned can be shown by introducing an auxiliary functional and a supplementary constrained variational problem.展开更多
基金supported by the National Natural Science Foundation of China (Nos.10801102, 0771151)the Sichuan Youth Sciences and Technology Foundation (No.07ZQ026-009) the China Postdoctoral Science Foundation
文摘This paper deals with the standing wave for a Hamiltonian nonlinear wave equation which can be viewed as a representative of the class of equations of interest.On the one hand,by proving a compactness lemma and solving a variational problem,the existence of the standing wave with ground state for the aforementioned equation is proved.On the other hand,the authors derive the instability of the standing wave by applying the potential well argument,the concavity method and an invariant region under the solution flow of the Cauchy problem for the equation under study,and the invariance of the region aforementioned can be shown by introducing an auxiliary functional and a supplementary constrained variational problem.
