Variational Methods for Nonlocal Fractional Problems

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.