7 Subelliptic problems on Carnot groups

Chapters in this book

1. Frontmatter I
2. Preface VII
3. Contents IX
4. Introduction XI
5. Part I: Elliptic equations in ℝ _N with nonstandard growth
6. 1 Critical quasilinear equations of Marcellini’s type 3
7. 2 On (p, N) Laplacian equations in ℝ^N with exponential nonlinearities 21
8. 3 Critical Hardy–Kirchhoff equations in ℝ^N 43
9. Part II: Existence of multiple solutions via group-theoretical invariance in the Hilbertian setting
10. 4 Multiple solutions for critical equations in ℝ^N 65
11. 5 Weak solutions of a scalar field equation 85
12. 6 Elliptic equations on the sphere 111
13. Part III: Variational Principles in Geometric Analysis
14. 7 Subelliptic problems on Carnot groups 145
15. 8 Arbitrarily many solutions on homogeneous Hadamard manifolds 173
16. 9 Kirchhoff problems on the Poincaré ball model 203
17. A Appendix – the symmetric criticality principle 241
18. List of symbols 247
19. Bibliography 249
20. Index 261