Perturbed minimization principles and applications

Given a bounded below, lower semi-continuous function f on an infinite dimensional Banach space or a non-compact manifold X, we consider various possibilities of perturbing f by an element p of a reasonable class of functions A in such a way that for the new functional f-p, the minimization problem inf _X (f-p) is well-posed (i.e., every minimizing sequence is convergent). These perturbed minimization principles are quite powerful and have a wide array of applications in Banach space theory, potential theory, non-smooth analysis, non-linear analysis, the variational approach to differential equations as well as in the theory of viscosity solutions for Hamilton-Jacobi equations.