A nonlinear wave equation with jumping nonlinearity

We investigate multiplicity of solutions u(x, t) for a piecewise linear per turbation of the one-dimensional wave operator u(tt) - u(xx) under Dirichle t boundary condition on the interval (-pi /2, pi /2, ) and periodic conditi on on the variable t. Our concern is to investigate a relation between mult iplicity of solutions and source terms of the equation when the nonlinearit y -(bu(+) - au(-)) crosses two eigenvalues and the source term f is generat ed by two eigenfunctions phi (00), phi 10.