Abstract In this paper,the existence of periodic solution for the third order nonlinear ordinary differential equation of the form x…+f()+g()+h(x)=p(t) is considered,where f,g,h and p are the continuous f...Abstract In this paper,the existence of periodic solution for the third order nonlinear ordinary differential equation of the form x…+f()+g()+h(x)=p(t) is considered,where f,g,h and p are the continuous functions,and p(t+T)=p(t). By using the Leray Schauder degree method,some sufficient conditions to guarantee the existence of T periodic solution for the equation are obtained.Some previous results are extended and improved.展开更多
Abstract By coincidence degree, the existence of solution to the periodic boundary value problem of functional differential equations with perturbation (t)=b(t,x t)+G(t,x t),\ 0≤t≤T, x(0)=x(T). is proved, where ...Abstract By coincidence degree, the existence of solution to the periodic boundary value problem of functional differential equations with perturbation (t)=b(t,x t)+G(t,x t),\ 0≤t≤T, x(0)=x(T). is proved, where x(t) ∈R n,x t∈BC(R,R n) are given by x t(s)=x(t+s), b and G are continuous mappings from ×BC (R,R n ) into R n and take bounded sets into bounded sets, b(t,φ) is linear with respect to φ∈BC (R,R n ). Furthermore, a similar result to the periodic boundary value problem of functional differential equations with infinite delay is established.展开更多
In this paper,a multi-point boundary value problems for a three order nonlinear deferential equation is considered.With the help of coincidence theorem due to Mawhin,a existence theorem is obtained.
文摘Abstract In this paper,the existence of periodic solution for the third order nonlinear ordinary differential equation of the form x…+f()+g()+h(x)=p(t) is considered,where f,g,h and p are the continuous functions,and p(t+T)=p(t). By using the Leray Schauder degree method,some sufficient conditions to guarantee the existence of T periodic solution for the equation are obtained.Some previous results are extended and improved.
文摘Abstract By coincidence degree, the existence of solution to the periodic boundary value problem of functional differential equations with perturbation (t)=b(t,x t)+G(t,x t),\ 0≤t≤T, x(0)=x(T). is proved, where x(t) ∈R n,x t∈BC(R,R n) are given by x t(s)=x(t+s), b and G are continuous mappings from ×BC (R,R n ) into R n and take bounded sets into bounded sets, b(t,φ) is linear with respect to φ∈BC (R,R n ). Furthermore, a similar result to the periodic boundary value problem of functional differential equations with infinite delay is established.
基金Supported by Nature Science Foundation of Education Department of Henan Province（2010A110023）
文摘In this paper,a multi-point boundary value problems for a three order nonlinear deferential equation is considered.With the help of coincidence theorem due to Mawhin,a existence theorem is obtained.
