Periodic boundary value problems for second order nonlinear coupled ordinary differential systems (Q1346464)

The author considers the system of differential equations \(-u''= f(t, u, v)+ p(t)\), \(-v''= g(t, u, v)+ q(t)\) with boundary conditions of the form \(u(0)= u(T)\), \(u'(0)= u'(T)\), \(v(0)= v(T)\), and \(V'(0)= v'(T)\). The functions \(f\), \(g\), \(p\) and \(q\) are assumed to be continuous on the respective domains. Existence of solutions for the above periodic boundary value problem is established under fairly general assumptions and the results generalize several known results.