Variational Principles in Mathematical Physics, Geometry, and Economics

Alexandru Kristály is Associate Professor in the Department of Economics at the University of Babeş-Bolyai in Cluj-Napoca, Romania. Vicenţiu D. Rădulescu is Professor in the Department of Mathematics at the University of Craiova, Romania. Csaba Gyorgy Varga is Professor in the Department of Mathematics at the University of Babeş-Bolyai in Cluj-Napoca, Romania.

'… an original attempt to rigorously introduce the principles of the calculus of variations underlying some interesting problems coming from various contexts: mathematical physics, geometry and optimization in economics. The main emphasis is placed on selected topics and their potential applications, since most of them have not been treated before in existing monographs.' Mathematical Reviews

• 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.