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.