On the bifurcation of large amplitude solutions for a system of wave and beam equations Original Research Article

We consider the existence of solutions for linearly coupled system of wave and beam equation with a sublinear perturbation. The main concept is the matrix spectrum which is a natural extension of the usual spectrum. Using the standard ‘change of degree’ argument we shall find necessary and sufficient conditions for the existence of asymptotic bifurcation with respect to the matrix spectrum both in one parameter and four parameter cases. Obviously the results can be modified for more general systems of partial differential equations.