A new index is constructed by use of the canonical representation of S1 × S1 group over a product space. This index satisfies the general properties of the usual index but does not satifsy the dimension property....A new index is constructed by use of the canonical representation of S1 × S1 group over a product space. This index satisfies the general properties of the usual index but does not satifsy the dimension property. As an application, two abstract critical point theorems are given.展开更多
By using the index theory for linear bounded self-adjoint operators in a Hilbert space related to a fixed self-adjoint operator A with compact resolvent,the authors discuss the existence and multiplicity of solutions ...By using the index theory for linear bounded self-adjoint operators in a Hilbert space related to a fixed self-adjoint operator A with compact resolvent,the authors discuss the existence and multiplicity of solutions for(nonlinear) operator equations,and give some applications to some boundary value problems of first order Hamiltonian systems and second order Hamiltonian systems.展开更多
文摘A new index is constructed by use of the canonical representation of S1 × S1 group over a product space. This index satisfies the general properties of the usual index but does not satifsy the dimension property. As an application, two abstract critical point theorems are given.
基金Project supported by the National Natural Science Foundation of China (Nos.11071127,10621101,10901118)the 973 project of the Ministry of Science and Technology of China (No.2011CB808002)
文摘By using the index theory for linear bounded self-adjoint operators in a Hilbert space related to a fixed self-adjoint operator A with compact resolvent,the authors discuss the existence and multiplicity of solutions for(nonlinear) operator equations,and give some applications to some boundary value problems of first order Hamiltonian systems and second order Hamiltonian systems.
