This paper deals with the existence of periodic solutions of a nonhomogeneous string with Dirichlet-Neumann condition. The authors consider the case that the period is irrational multiple of space length and prove tha...This paper deals with the existence of periodic solutions of a nonhomogeneous string with Dirichlet-Neumann condition. The authors consider the case that the period is irrational multiple of space length and prove that for some irrational number, zero is not the accumulation point of the spectrum of the associated linear operator. This result can be used to prove the existence of the periodic solution avoid using Nash-Moser iteration.展开更多
We investigate solutions to superlinear or sublinear operator equations and obtain some abstract existence results by minimax methods. These results apply to superlinear or sublinear Hamiltonian systems satisfying sev...We investigate solutions to superlinear or sublinear operator equations and obtain some abstract existence results by minimax methods. These results apply to superlinear or sublinear Hamiltonian systems satisfying several boundary value conditions including Sturm-Liouville boundary value conditions and generalized periodic boundary value conditions, and yield some new theorems concerning existence of solutions or nontrivial solutions. In particular, some famous results about periodic solutions to superlinear or sublinear Hamiltonian systems by Rabinowitz or Benci and Rabinowitz are special cases of the theorems.展开更多
基金supported by the Zhejiang Provincial Department of Education Research Fund(No.Y201326873)
文摘This paper deals with the existence of periodic solutions of a nonhomogeneous string with Dirichlet-Neumann condition. The authors consider the case that the period is irrational multiple of space length and prove that for some irrational number, zero is not the accumulation point of the spectrum of the associated linear operator. This result can be used to prove the existence of the periodic solution avoid using Nash-Moser iteration.
基金supported by National Natural Science Foundation of China(Grant No.11171157)the Jiangsu Planned Projects for Postdoctoral Research Funds
文摘We investigate solutions to superlinear or sublinear operator equations and obtain some abstract existence results by minimax methods. These results apply to superlinear or sublinear Hamiltonian systems satisfying several boundary value conditions including Sturm-Liouville boundary value conditions and generalized periodic boundary value conditions, and yield some new theorems concerning existence of solutions or nontrivial solutions. In particular, some famous results about periodic solutions to superlinear or sublinear Hamiltonian systems by Rabinowitz or Benci and Rabinowitz are special cases of the theorems.
