Dimitrios C. Kravvaritis & Athanasios N. Yannacopoulos 
Variational Methods in Nonlinear Analysis [PDF ebook] 
With Applications in Optimization and Partial Differential Equations

This well-thought-out book covers the fundamentals of nonlinear analysis, with a particular focus on variational methods and their applications. Starting from preliminaries in functional analysis, it expands in several directions such as Banach spaces, fixed point theory, nonsmooth analysis, minimax theory, variational calculus and inequalities, critical point theory, monotone, maximal monotone and pseudomonotone operators, and evolution problems.