A thorough graduate-level introduction to the variational analysis of nonlinear problems described by nonlocal operators.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
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.
Inhaltsangabe
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.
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.
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