An Application of Category Theory to a Class of the Systems of the Superquadratic Wave Equations

摘要

We investigate the nontrivial solutions for a class of the systems of the superquadratic nonlinear wave equations with Dirichlet boundary condition and periodic condition: u_(tt) - u_(xx) = av + F_u(x,t,u,υ) in (- π/2,π/2) × R, υ_(tt) - v(xx) = bu + F_υ(x, t,u, υ) in (-π/2,π/2) x R, u(±π/2,t) = υ(±π/2,t) (1.1).