The famous Tricomi equation was established in 1923, by F. G. Tricomi, who is the pioneer
of parabolic elliptic and hyperbolic boundary value problems and related problems of variable
type. In 1945, F. I. Frankl established a generalization of these problems for the well-known
Chaplygin equation. In 1953 and 1955, M. H. Protter generalized these problems even further.
In 1977, we generalized these results in several n-dimensional simply connected domains. In
1950-1951, M. A. Lavrentjev and A. V. Bitsadze investigated the Bitsadze - Lavrentjev equa-
tion. In 1990, we proposed the exterior Tricomi problem. In 2002, we considered uniqueness
of quasi-regular solutions for a bi-parabolic elliptic bi-hyperbolic Tricomi problem. In 2006,
G. C. Wen investigated the exterior Tricomi problem for general mixed type equations. In
2011, we established the exterior Tricomi and Frankl problems for quaterelliptic - quaterhyper-
bolic equations. In 2014, D. Amanov and J. M. Rassias investigated boundary value problems
for the higher order generalized mixed-parabolic equation. In this paper we investigate the
exterior Bitsadze-Lavrentjev problem for quaterelliptic -quaterhyperbolic Bitsadze-Lavrentjev
PDEquations with eight parabolic lines in a doubly connected domain and propose open prob-
lems. These problems are of vital importance in
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 G. Barantsev On singularities of the Tricomi problem solution by the Fourier method
Teubner-Texte zur Mathematik (Ed. J. M. Rassias) Vol. 90 Leipzig 1986 pp. 47-54.
 G. Fichera Francesco Giacomo Tricomi Teubner-Texte zur Mathematik (Ed. J. M. Rassias)
Vol. 79 Leipzig 1985 pp. 6-31.
 F. I. Frankl On the problems of Chaplygin for mixed subsonic and supersonic
Akad. Nauk SSSR Ser. Mat. 9 (1945) 121-143.
 M. Kracht and E. Kreyszig The Tricomi equation and transition problems Teubner-Texte
zur Mathematik (Ed. J. M. Rassias) Vol. 90 Leipzig 1986 pp. 157-165.
 E. Kreyszig Introductory Functional Analysis with Applications Wiley New York 1989.
 E. Kreyszig Banach spaces in Bergman Operator TheoryWorld Scientific (Ed. J. M. Rassias)
Singapore 1994 pp. 155-165.
 M. H. Protter Uniqueness theorems for the Tricomi problem I II J.Rat. Mech. Anal. 2
(1953) 107-114; 4(1955) 721-732.
 J. M. Rassias Mixed type partial differential equations in Rn Ph.D. dissertation U.C. Berkeley
 J. M. Rassias A maximum principle in Rn+1 J. Math. Anal. & Appl. Acad. Press New
York 85 (1982) 106-113.
 J. M. Rassias On the Tricomi problem with two parabolic lines of degeneracy Bull. Inst.
Math. Acad. Sinica 12 (1983) 62-67.
 J. M. Rassias Lecture Notes on Mixed Type Partial Differential Equations World Scientific
 J. M. Rassias On the Well-posed Tricomi problem in R2 Discuss. Math. 12 (1992) 85-93.
 J. M. Rassias Uniqueness of Quasi-regular Solutions for a parabolic elliptic-hyperbolic Tricomi
problem Bull. Inst. Math. Acad. Sinica 25 (1997) 277-287.
 J. M. Rassias Advances in Equations and Inequalities Hadronic Press Inc. Palm Harbor
FL. U.S.A. 1999.
 J. M. Rassias Existence of Weak Solutions for a parabolic elliptic-hyperbolic Tricomi problem
Tsukuba J. Math. 23(1999) 37-54.
 J. M. Rassias Uniqueness of Quasi-Regular Solutions for a Bi-Parabolic Elliptic Bi-hyperbolic
Tricomi Problem Complex Variables and Elliptic Equations 47(8) (2002) 707-718.
 J. M. Rassias and G. C. Wen Solvability of the Oblique Derivative Problem for Second Order
Equations of Mixed Type with Nonsmooth Degenerate Curve Intern. J. Appl. Math. Stat.
 R. I. Semerdjieva Uniqueness of regular solutions for a class of non-linear degenerating hy-
perbolic equations Math. Balk. 7 (1993) 277-283.
 F. G. Tricomi Sulle equazioni lineari alle parziali di 20 ordine di tipo misto Atti Accad. Naz.
Lincei 14 (1923) 133-247.
 G. C. Wen The Exterior Tricomi Problem for Generalized Mixed Equations with Parabolic
Degeneracy Acta Math. Sinica 22(5)(2006) 1385-1398.
 G. C. Wen Oblique Derivative Problems for General Chaplygin-Rassias Equations with
Nonsmooth Degenerate Line in Mixed Domains Science in China Series A: Mathematics
 G. C.Wen The Tricomi and Frankl Problems for Generalized Chaplygin Equations in Multiply
Connected Domains Acta Math. Sin. 24(11) 1759-1774.
 G. C. Wen Oblique Derivative Problems for Generalized Rassias Equations of Mixed Type
with Several Characteristic Boundaries Electr. J. Diff. Equations 2009(65)(2009) 1-16.
 G. C. Wen Elliptic Hyperbolic and Mixed Complex Equations with Parabolic Degeneracy [
Including Tricomi-Bers and Tricomi-Frankl-Rassias Problems] World Scientific Co. Pte. Ltd.
Singapore : Peking University Series in Mathematics - Vol. 4 2008 1-439.
 G. C. Wen and H. Begehr Boundary Value Problems for Elliptic Equations and Systems
Longman Scientific and Technical Company Harlow1990.
 G. C. Wen D. C. Chen and X. Cheng General Tricomi-Rassias Problem and Oblique Deriva-
tive Problem for generalized Chaplygin Equation J. Math. Anal. 333 (2007) 679-694.
 G. C. Wen and D. C. Chen Discontinuous Riemann-Hilbert Problems for Degenerate Elliptic
Complex Equations of First Order Complex Variables 50(2005) 707-718.
 G. C. Wen and Z. T. Ma Discontinuous Oblique Derivative Problem for Second Order Equa-
tions of Mixed Type in General Domains Complex Variables 48(2)(2003) 119-130.
 M. A. Lavrentjev and A. V. Bitsadze On the Problem of the Equations of the Mixed Type
Dokl. Akad. Nauk. SSSR 70 (3) (1950) 373-376.
 A. V. Bitsadze On the Problem of Equations of the Mixed Type Doctoral Thesis: Library of
the Mat. Inst. Akad. Nauk. SSSR (1951).
 G. C. Wen (Chief Editor) Boundary Value Problems Integral Equations and Related Topics
Proc. of 3rd Int. Conf. 2011 World Sci. Publ. Co. Pte. Ltd.
 J. M. Rassias The Exterior Tricomi and Frankl Problems for Quaterelliptic-Quaterhyperbolic
Equations with Eight Parabolic Lines European J. Pure and Appl. Math. 4(2)(2011) 186-
 J. M. Rassias Uniqueness of Solutions for the Exterior Quaterelliptic-Quaterhyperbolic Tri-
comi Problem with Eight Parabolic Lines In: Boundary Value Problems Integral Equations
and Related Topics Proceedings of the Third International Conference World Sci. Publ. Co.
Pte. Ltd. 2011(1) 58-71.
 D. Amanov and J. M. Rassias Boundary value problems for the higher order generalized
mixed-parabolic equation with fractional derivatives Contemporary Analysis and Applied
Mathematics 2(2) (2014) 198-211.