Some theorems are obtained for the existence of nontrivial solutions of Hamiltonian systems with Lagrangian boundary conditions by the minimax methods.
In this paper, the authors study the existence of nontrivial solutions for the Hamiltonian systems z（t） = J△↓H（t, z（t）） with Lagrangian boundary conditions, where ^H（t,z）=1/2（^B（t）z, z） ＋ ^H（t, z）,^B...In this paper, the authors study the existence of nontrivial solutions for the Hamiltonian systems z（t） = J△↓H（t, z（t）） with Lagrangian boundary conditions, where ^H（t,z）=1/2（^B（t）z, z） ＋ ^H（t, z）,^B（t） is a semipositive symmetric continuous matrix and ^H（t, z） = satisfies a superquadratic condition at infinity. We also obtain a result about the L-index.展开更多
By weakening or dropping the superquadraticity condition （SQC）, the existence of positive solutions for a class of elliptic equations is established. In particular, we deal with the asymptotieal linearities as well ...By weakening or dropping the superquadraticity condition （SQC）, the existence of positive solutions for a class of elliptic equations is established. In particular, we deal with the asymptotieal linearities as well as the superlinear nonlinearities.展开更多
The author proves a sharper estimate on the minimal period for periodic solutions of autonomous second order Hamiltonian systems under precisely Rabinowitz' superquadratic condition.
基金supported by the National Natural Science Foundation of China and 973 Program of STM.
文摘Some theorems are obtained for the existence of nontrivial solutions of Hamiltonian systems with Lagrangian boundary conditions by the minimax methods.
基金supported by the National Natural Science Foundation of China (Nos. 10531050, 10621101)the 973 Project of the Ministry of Science and Technology of China.
文摘In this paper, the authors study the existence of nontrivial solutions for the Hamiltonian systems z（t） = J△↓H（t, z（t）） with Lagrangian boundary conditions, where ^H（t,z）=1/2（^B（t）z, z） ＋ ^H（t, z）,^B（t） is a semipositive symmetric continuous matrix and ^H（t, z） = satisfies a superquadratic condition at infinity. We also obtain a result about the L-index.
文摘By weakening or dropping the superquadraticity condition （SQC）, the existence of positive solutions for a class of elliptic equations is established. In particular, we deal with the asymptotieal linearities as well as the superlinear nonlinearities.
文摘The author proves a sharper estimate on the minimal period for periodic solutions of autonomous second order Hamiltonian systems under precisely Rabinowitz' superquadratic condition.
