Introduction .................................................... 1
Chapter 1 Preliminaries ........................................ 5
Chapter 2 Basic Solutions ...................................... 9
2.1 Properties of basic solutions .............................. 9
2.2 The spectral equation and Spec( 0) ........................ 11
2.3 Existence of basic solutions .............................. 13
2.4 Properties of the fundamental matrix of (Eσ ) ............. 14
2.5 The system of equations for the adjoint operator * ...... 16
2.6 Continuation of a simple spectral value ................... 17
2.7 Continuation of a double spectral value ................... 19
2.8 Purely imaginary spectral value ........................... 22
2.9 Main result about basic solutions ......................... 24
Chapter 3 Example ............................................. 27
Chapter 4 Asymptotic behavior of the basic solutions of ..... 29
4.1 Estimate of σ ............................................. 30
4.2 First estimate of Φ and ψ ................................. 33
4.3 End of the proof of Theorem 4.1 ........................... 34
Chapter 5 The kernels ......................................... 37
5.1 Two lemmas ................................................ 38
5.2 Proof of Theorem 5.1 ...................................... 40
5.3 Modified kernels .......................................... 41
Chapter 6 The homogeneous equation u = 0 ..................... 43
6.1 Representation of solutions in a cylinder ................. 43
6.2 Cauchy integral formula ................................... 46
6.3 Consequences .............................................. 47
Chapter 7 The nonhomogeneous equation u = F .................. 51
7.1 Generalized Cauchy Integral Formula ....................... 51
7.2 The integral operator T ................................... 52
7.3 Compactness of the operator T ............................. 55
Chapter 8 The semilinear equation ............................. 57
Chapter 9 The second order equation: Reduction ................ 61
Chapter 10 The homogeneous equation Pu = 0 ..................... 63
10.1 Some properties .......................................... 63
10.2 Main result about the homogeneous equation Pu = 0 ........ 65
10.3 A maximum principle ...................................... 67
Chapter 11 The nonhomogeneous equation Pu = F .................. 69
Chapter 12 Normalization of a Class of Second Order Equations
with a Singularity .................................. 73
Bibliography ................................................... 77
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