In this paper,we study the existence and multiplicity of homoclinic solutions for a class of second-order Hamiltonian system:u″(t)−L(t)u(t)+▽V(t,u)=0,where L(t)and V(t,u)are not periodic in t.First,we introduce the ...In this paper,we study the existence and multiplicity of homoclinic solutions for a class of second-order Hamiltonian system:u″(t)−L(t)u(t)+▽V(t,u)=0,where L(t)and V(t,u)are not periodic in t.First,we introduce the definition of index and establish the corresponding index theory.Then,by using the index theory and critical point theory,we prove our main results under the asymptotic quadratic conditions of the potential function.展开更多
基金Supported by the Fundamental Research Funds for the Central Universities(Grant No.2019XKQYMS91)。
文摘In this paper,we study the existence and multiplicity of homoclinic solutions for a class of second-order Hamiltonian system:u″(t)−L(t)u(t)+▽V(t,u)=0,where L(t)and V(t,u)are not periodic in t.First,we introduce the definition of index and establish the corresponding index theory.Then,by using the index theory and critical point theory,we prove our main results under the asymptotic quadratic conditions of the potential function.
