# On First and Second Order Planar Elliptic Equations with Degeneracies

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*Abdelhamid Meziani*

#### Table of Contents

# Table of Contents

## On First and Second Order Planar Elliptic Equations with Degeneracies

- Introduction 18 free
- Chapter 1. Preliminaries 512 free
- Chapter 2. Basic Solutions 916
- 2.1. Properties of basic solutions 916
- 2.2. The spectral equation and Spec(L0) 1118
- 2.3. Existence of basic solutions 1320
- 2.4. Properties of the fundamental matrix of (E,) 1421
- 2.5. The system of equations for the adjoint operator L* 1623
- 2.6. Continuation of a simple spectral value 1724
- 2.7. Continuation of a double spectral value 1926
- 2.8. Purely imaginary spectral value 2229
- 2.9. Main result about basic solutions 2431

- Chapter 3. Example 2734
- Chapter 4. Asymptotic behavior of the basic solutions of L 2936
- Chapter 5. The kernels 3744
- Chapter 6. The homogeneous equation L u=0 4350
- Chapter 7. The nonhomogeneous equation L u=F 5158
- Chapter 8. The semilinear equation 5764
- Chapter 9. The second order equation: Reduction 6168
- Chapter 10. The homogeneous equation Pu=0 6370
- Chapter 11. The nonhomogeneous equation Pu=F 6976
- Chapter 12. Normalization of a Class of Second Order Equations with a Singularity 7380
- Bibliography 7784