Variational Methods for Nonlocal Fractional Problems

Giovanni Molica Bisci is Assistant Professor of Mathematical Analysis at the Università 'Mediterranea' di Reggio Calabria. He is the author of more than 90 research papers in nonlinear analysis.

A thorough graduate-level introduction to the variational analysis of nonlinear problems described by nonlocal operators.

Foreword Jean Mawhin; Preface; Part I. Fractional Sobolev Spaces: 1. Fractional framework; 2. A density result for fractional Sobolev spaces; 3. An eigenvalue problem; 4. Weak and viscosity solutions; 5. Spectral fractional Laplacian problems; Part II. Nonlocal Subcritical Problems: 6. Mountain Pass and linking results; 7. Existence and localization of solutions; 8. Resonant fractional equations; 9. A pseudo-index approach to nonlocal problems; 10. Multiple solutions for parametric equations; 11. Infinitely many solutions; 12. Fractional Kirchhoff-type problems; 13. On fractional Schrödinger equations; Part III. Nonlocal Critical Problems: 14. The Brezis¿Nirenberg result for the fractional Laplacian; 15. Generalizations of the Brezis¿Nirenberg result; 16. The Brezis¿Nirenberg result in low dimension; 17. The critical equation in the resonant case; 18. The Brezis¿Nirenberg result for a general nonlocal equation; 19. Existence of multiple solutions; 20. Nonlocal critical equations with concave-convex nonlinearities; References; Index.