A comprehensive introduction to modern applied functional analysis. Assumes only basic notions of calculus, real analysis, geometry, and differential equations.

Alexandru Kristály is Associate Professor in the Department of Economics at the University of Babe¿-Bolyai in Cluj-Napoca, Romania.

Foreword Jean Mawhin; Preface; Part I. Variational Principles in Mathematical Physics: 1. Variational principles; 2. Variational inequalities; 3. Nonlinear eigenvalue problems; 4. Elliptic systems of gradient type; 5. Systems with arbitrary growth nonlinearities; 6. Scalar field systems; 7. Competition phenomena in Dirichlet problems; 8. Problems to Part I; Part II. Variational Principles in Geometry: 9. Sublinear problems on Riemannian manifolds; 10. Asymptotically critical problems on spheres; 11. Equations with critical exponent; 12. Problems to Part II; Part III. Variational Principles in Economics: 13. Mathematical preliminaries; 14. Minimization of cost-functions on manifolds; 15. Best approximation problems on manifolds; 16. A variational approach to Nash equilibria; 17. Problems to Part III; Appendix A. Elements of convex analysis; Appendix B. Function spaces; Appendix C. Category and genus; Appendix D. Clarke and Degiovanni gradients; Appendix E. Elements of set-valued analysis; References; Index.