一类广义Schr?dinger型非线性高阶方程组

In this paper we consider a class of semilinear systems of partial differential equations of higher order A(t)u₁+(-1)^Mu_x^ZM=f(u), which contain a class of the nonlinear Schr?dinger equations, where the matrix A(t) is nonsingular, nonnegative definite and f(u) satisfy the conditions (i) f(u) = -grad F(u), F(u)≥0(ii) (g(u),u)≤α(u,u) + b, g = A^－1f. The existence, uniqueness and regularity of solutions for periodic boundary problems and Cauchy problems in global are proved.

A Class of Generalized Nonlinear Schr?dinger Systems of Higher Order