Bifurcation of Solutions to a Nonlinear Elliptic Problem in a Disk

We study a nonlinear elliptic Dirichlet boundary value problem for an equation in a circular domain. Using the method of small parameters and the Lyapunov–Schmidt reduction, we investigate bifurcation points, construct asymptotic expansions of solutions, and determine the nature of the emerging branches. The existence of a supercritical pitchfork bifurcation is proved. The stability of solutions and the global structure of branches are analysed.