Elliptic, Hyperbolic and Mixed Complex Equations with Parabolic Degeneracy: Including Tricomi-Bers and Tricomi-Frankl-Rrassias Problems (Peking University Series in Mathematics)
The method revealed in this book is unlike any other, in which the hyperbolic number and hyperbolic complex function in hyperbolic domains, and the complex number and complex function in elliptic domains are used. The corresponding problems for first order complex equations with singular coefficients are first discussed, and then the problems for second order complex equations are considered, where we pose the new partial derivative notations and complex analytic methods such that the forms of the above first order complex equations in hyperbolic and elliptic domains are wholly identical. In the meantime, the estimates of solutions for the above problems are obtained, hence many open problems including the above Tricomi Bers and Tricomi Frankl Rassias problems can be solved.
Contents: Elliptic Complex Equations of First Order; Elliptic Complex Equations of Second Order; Hyperbolic Complex Equations of First and Second Orders; First Order Complex Equations of Mixed Type; Second Order Linear Equations of Mixed Type; Second Order Quasilinear Equations of Mixed Type.
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Approaches to the Qualitative Theory of Ordinary Differential Equations: Dynamical Systems and Nonlinear Oscillations (Peking University Series in Mathematics)
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