The branch of positive solutions to a semilinear elliptic equation on
The existence of the Hopf bifurcation for parabolic functional equations with delay of maximum order in spatial derivatives is proved. An application to an integrodifferential equation with a singular kernel is given.
In this paper, we are interested in the study of bifurcation solutions of nonlinear wave equation of elastic beams located on elastic foundations with small perturbation by using local method of Lyapunov-Schmidt.We showed that the bifurcation equation corresponding to the elastic beams equation is given by the nonlinear system of two equations. Also, we found the parameters equation of the Discriminant set of the specified problem as well as the bifurcation diagram.