An Introduction to Minimax Theorems and Their Applications to Differential Equations

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This text is intended to be an introduction to critical point theory and its applications to differential equations. Although the related material can be found in other books, the authors of this volume have had the following goals in mind: to present a survey of existing minimax theorems; to give applications to elliptic differential equations in bounded domains; to consider the dual variational method for problems with continuous and discontinuous nonlinearities; to present some elements of critical point theory for locally Lipschitz functionals and give applications to fourth-order differential equations with discontinuous nonlinearities; and to study homoclinic solutions of differential equations via the variational methods.