Ljusternik-Schnirelman minimax algorithms and an application for finding multiple negative energy solutions of semilinear elliptic Dirichlet problem involving concave and convex nonlinearities. I: Algorithms and convergence (Q283281)

The paper under review establishes two minimax algorithms related to the Ljusternik-Schnirelman theory, which is a central tool in critical point theory. Related global sequence convergence properties are also proved in this paper. The final section contains a numerical experiment to calculate multiple negative energy solutions of a semilinear elliptic equation with Dirichlet boundary condition.