Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 65, pp. 1-16.

Title:  Oblique derivative problems for  generalized Rassias equations 
        of mixed type with several characteristic boundaries
   
Author: Guo Chun Wen  (Peking Univ., Beijing, China)

Abstract:
 This article concerns the oblique derivative problems for
 second-order quasilinear degenerate equations of mixed type with
 several characteristic boundaries, which include the Tricomi problem
 as a special case. First we formulate the problem
 and obtain estimates of its solutions, then we show the existence
 of solutions by the successive iterations and the Leray-Schauder theorem.
 We use a complex analytic method: elliptic complex functions
 are used in the elliptic domain, and hyperbolic complex functions
 in the hyperbolic domain, such that  second-order equations of mixed
 type with degenerate curve are reduced to the first order mixed complex
 equations with singular coefficients.
 An application of the complex analytic method, solves
 (1.1) below with $m=n=1$, $a=b=0$, which was posed as
 an open problem  by Rassias. 
 
Submitted December 16, 2008. Published May 14, 2009.
Math Subject Classifications: 35M05, 35J70, 35L80.
Key Words: Oblique derivative problems; generalized Rassias equations;
           several characteristic boundaries.