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 Ordinary Differential Equations A quasilinearization method for the construction of an approximate solution of a certain boundary value problem for ordinary differential equationsI. I. Bezvershenko 195 The limit cycles of a certain differential equationG. M. Buldyk 200 Dynamical systems with invariant Lebesgue measure on connected, closed and orientable surfacesN. I. Gavrilov 206 The escape of a certain nonlinear object from several more inert pursuersP. B. Gusyatnikov 213 The resolvent and fractional powers of ordinary differential operators in spaces of smooth functionsI. D. Evzerov, P. E. Sobolevskii 227 A theorem on critical cases of systems of difference equationsN. I. Kazeeva, S. N. Shimanov 234 The complete qualitative investigation of Duffing's equationA. D. Morozov 241 Symbolic dynamics that are generated by homoclinic structuresYu. I. Neimark 256 The problem of discrimination for the normal domain $N_4$ in the space $R^3$S. K. Norkin 263 Higher order singularly degenerate differential operators with unbounded operator coefficientsV. P. Orlov 272 Algebraic invariants of multidimensional differential systemsK. S. Sibirskii, V. D. Taku 281 Conditions for a center for a certain Liénard equationL. A. Cherkas 292 The singular nonlinear boundary value problem for a second-order equation with a rapidly growing right-hand sideG. V. Sherbina 299 Partial Differential Equations A mixed problem for a hyperbolic system in spaceA. I. Vahabov 305 Characteristic problems with a principal part that contains mixed derivativesA. A. Iosif'yan 309 Asymptotic behavior with respect to time for the solutions of a strongly parabolic system with discontinuous coefficientsYa. I. Kanel' 325 The Cauchy problem for certain abstract hyperbolic equations of evenorderYa. V. Radyno, N. J. Yurchuk 331 The normal solvability of the Dirichlet problem for a certain degenerate elliptic systemR. M. Sharipova 343 Short Communications A geometric method of solving systems of differential equationsS. P. Blinov 348 The asymptotic behavior of the solutions of a certain system of differential equations in the neighborhood of a singular pointA. E. Zernov 352 Stability of a trajectoryV. I. Zubov 354 Eigenvalues of a periodic boundary value problem for certain partial differential equationsV. S. Mokeichev 356 The approximability property of regular systems of linear differential equationsG. N. Petrovskiĭ 359 The solvability of operator-differential equations of arbitrary orderV. G. Raskin 362 The approximate representation of relaxation oscillationsG. V. Sugrobov 365 A method of solving Abel and Riccati equationsF. G. Tempel' 369 A priori estimates and nonlocal existence theorems for the solutions of quasilinear parabolic equations in $L_p$ spacesA. I. Yasakov 372 Chronicle IV Âñåñîþçíàÿ êîíôåðåíöèÿ ïî òåîðèè è ïðèëîæåíèÿì äèôôåðåíöèàëüíûõ óðàâíåíèé ñ îòêëîíÿþùèìñÿ àðãóìåíòîìYu. A. Mitropol'skii, E. Yu. Romanenko 375