Introduction .................................................... 1
Chapter 1. Bifurcation diagrams ................................. 7
Chapter 2. Oscillation properties .............................. 13
Chapter 3. Ground states ....................................... 37
3.1. Existence ...................................... 37
3.2. Uniqueness ..................................... 37
Chapter 4. Stability of thermal structures ..................... 43
4.1. Stability ...................................... 43
4.2. Unstability .................................... 44
Chapter 5. Proof of main theorems .............................. 47
Chapter 6. The degenerate case, k = -1 ......................... 53
Chapter 7. Appendix 1. The conservative case (N = 1) ........... 63
Chapter 8. Appendix 2. Pohozaev Identity ....................... 69
Bibliography ................................................... 71
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