A brief reviev S. D. Eidelman results of the investigation for nonlinear problems is presented. We consider also papers deals with study quasilinear parabolic systems with degeneration on the initial hyperplane and quasilinear ultraparabolic equations. The local solvability theorem for the Cauchy problem for a quasilinear ultraparabolic equation with homogenous initial condition is proved and some global solvability results for theese equations is presented too.

[1] Eidelman S.D. Some theorems about linear and quasilinear parabolic systems // Proc. of XIII reporting scientific session of the Chernivtsi State University. - Chernivtsi, 1957. - P. 204-205.

[2] Eidelman S.D. On the Cauchy problem for nonlinear and quasilinear parabolic systems // Dokl. of the USSR Academy of Sciences. - 1957. -116, № 6. - P. 930-932.

[3] Eidelman S.D.About some applications of fundamental matrices of solutions of parabolic systems // Theoretical and Applied Mathematics. - Lviv, 1958. - Vyp.1. - P. 99-149

[4] Eidelman S.D., Ivasishen S.D. On the Cauchy problem for one class of nonlinear parabolic systems // Dokl. of the USSR Academy of Sciences. - 1961. -136, № 2. - P. 304-307.

[5] Eidelman S.D. Parabolic systems. -Moscow: Nauka, 1964. - 443 p.

[6] Eidelman S.D.About one class of parabolic systems // Dokl. of the USSR Academy of Sciences. - 1960. -133, № 1. - P. 40-43.

[7] Ivasishen S.D., Eidelman S.D. $\vec 2b$ - parabolic systems // Proc. of Seminar on Functional Analysis. - Kiev: Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, 1968. - Vyp.1. - P. 3-175, 271-273.

[8] Kondratyev, V.A.; Eidelman, S.D. About some properties of positive solutions of evolutionary hypoelliptic equations  // Dokl. of ANSSR. - 1969. -184, № 5. - P.1027-1030.

[9] Kondratyev, V.A.; Eidelman, S.D. On the nature of solutions of linear evolutionary systems with an elliptic spatial part  // Dokl. of the USSR Academy of Sciences. - 1969. -189, № 3. - P. 468-471.

[10] Kondratyev, V.A.; Eidelman, S.D. About positive solutions of some quasilinear equations // Dokl. of Sci. - 1993. -331, № 3. - P. 278-280.

[11] Kondratyev, V.A.; Eidelman, S.D. About positive solutions of quasilinear elliptic equations of the second order  // Dokl. of Sci. -1994. -334, № 4. - P. 427-428.

[12] Kondrat’ev V.А.,Еidelman S.D. Positive solutions of quasilinear Emden-Fauler systems of arbitrary order // Russ. J. Math. Phys. – 1994. – 2 , № 4. – P. 535–540.

[13] Еidelman S.D. On positive solutions of Emden-Fauler systems of an arbitrary order // Nonlinear boundary value problems. – 1997. – № 7. – P. 74–81.

[14] Eidelman S.D., Ivasyshen S.D., Kochubei A.N. Analytic methods in the theory of differential and pseudodifferential equations of parabolic type // Operator Theory: Adv. and Appl. – 2004. – 152. – 390 p.

[15] Medynsky I.P. On the local solvability of the Cauchy problem for a quasilinear parabolic system with weak degeneracy on the initial hyperplane // Bulletin of the National University ‘Lviv Polytechnic’. № 411. Applied mathematics. - Lviv, 2000. - P. 241-247.

[16] Medynskyi I.P. Cauchy problem for quasilinear parabolic systems with degeneracy on the initial hyperplane // Scientific Bulletin of Chernivtsi University: Collection of scientific papers. Mathematics - Chernivtsi: Ruta, 2001. - P. 90-95.

[17] Ivasyshen S.D., Medynskyi I.P. Local solvability of the Cauchy problem for a quasilinear - $\vec 2b$-parabolic system with weak degeneracy on the initial hyperplane  // Mathematical methods and physical and mechanical fields - 2004. - 47,  №  4. - P. 110-114.

[18] Ivasishen S.D., Androsova L.N. Fundamental solutions of the Cauchy problem for one class of emerging parabolic equations. - Chernovtsy University. - Chernivtsi, 1989. - 62 с. -Dep. in Ukr-NIINTI 16.06.89, № 1762-Uk89.

[19] Drone V.S., Ivasyshen S.D. On the property of the volume potential and the correct solvability of the Cauchy problem for one model ultraparabolic equation // Scientific Bulletin of Chernivtsi University: Collection of scientific papers. Mathematics - Chernivtsi: Ruta, 1999, p. 36-43.

[20] Ivasyshen S.D., Medynskyi I.P. On global solutions of the Cauchy problem for quasilinear parabolic equations // Mathematical methods and physical and mechanical fields. 1999. - 42, № 2. - P. 31-38.

[21] Medinsky I., Ivasishen C. On global solutions of the Cauchy problem for some quasi-linear ultraparabolic equations // International Mathematical Conf. named after V.Y. Skorobogatko, 24-28 September. 2007, Drohobych: abstracts - Lviv, 2007. - P. 189.

[22] Ivasyshen S.D., Medynskyi I.P. On the Cauchy problem for one quasilinear ultraparabolic equation of Kolmogorov type // Fourth All-Ukrainian Scientific Conference "Nonlinear Problems of Analysis", 10-12 September. 2008, Ivano-Frankivsk: abstracts - Ivano-Frankivsk, 2008. - P. 39.