Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials.

Intro -- Contents -- Chapter 1. Introduction -- 1.1. Background and aims -- 1.2. Our framework -- 1.3. On Vázquez-Véron's open question -- 1.4. An outline of our results -- 1.5. Acknowledgements -- Chapter 2. Main results -- 2.1. The subcritical parameter -- 2.2. The critical parameter -- Chapter 3. Radial solutions in the power case -- 3.1. The subcritical parameter -- 3.2. The critical parameter -- Chapter 4. Basic ingredients -- 4.1. A priori estimates -- 4.2. A Harnack-type inequality -- 4.3. A regularity lemma -- Chapter 5. The analysis for the subcritical parameter -- 5.1. Proof of Theorem 2.1 -- 5.2. Proof of Theorem 2.2 -- 5.3. Proof of Theorem 2.3 -- 5.4. Proof of Theorem 2.4 -- Chapter 6. The analysis for the critical parameter -- 6.1. Proof of Theorem 2.5 -- 6.2. Proof of Theorem 2.6 -- 6.3. Proof of Theorem 2.7 -- Chapter 7. Illustration of our results -- 7.1. On a prototype model -- 7.2. In other settings -- Appendix A. Regular variation theory and related results -- A.1. Properties of regularly varying functions -- A.2. Other results -- Bibliography.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.