Some Minimax Theorems and Applications to Nonlinear Partial Differential Equations.

摘要

Using minimax methods, some existence theorems are proved for critical points of a real valued function on a Banach space. The critical points are of a saddle point type. Applications are made to semilinear elliptic partial differential equations. A perturbation theorem for the critical points is also proved in this context. Lastly applications are made to a family of nonlinear wave equations.