VARIATIONAL METHODS FOR POTENCIAL OPERATOR EQUATIONS

Assuming some familiarity with functional analysis, nonlinear partial differential equations, and the theory of Sobolev spaces, Chabrowski (U. of Queensland) presents methods and problems of the variational calculus directly related to the theory of differential equations of elliptic type. These methods can be applied to nonlinear wave equations, Hamiltonian systems, and problems relevant to surfaces of prescribed mean curvature. Chapters cover: constrained minimization, applications of Lusternik-Schnirelman theory, nonhomogeneous potentials, potentials with covariance conditions, eigenvalues and level sets, generalizations of the (intriguingly named) mountain pass theorem, nondifferentiable functionals, and the concentration- compactness principle. An appendix helpfully furnishes some of the knowledge prerequisites