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 On the theory of equations of mixed typeA. V. Bitsadze 3 A lower bound of the sum of the squares of the fundamental functions, and of the number of the fundamental values, for an arbitrary $FSF$ of Laplace's operatorV. A. Il'in 7 Certain models connected with Euler's equationsA. A. Dezin 17 Inverse problems of generalized magnetic potentialsA. I. Prilepko 27 Exterior contact inverse problems of generalized magnetic potentials of variable densitiesA. I. Prilepko 39 Certain estimates of the solutions of nonlinear equations of mixed typeD. K. Gvazava 50 The principle of limiting amplitude for the Cauchy-Poisson problem in a strip. IE. K. Isakova 56 The Dirichlet problem for a certain class of elliptic systems of second order differential equationsR. S. Saks 72 Normal solvability of the Dirichlet problem for a certain class of systems of elliptic typeNguyen Thya Hop 86 A boundary value problem for equations of mixed type with two intersecting curves of degeneracyM. M. Zainulabidov 99 A certain boundary value problem for vortical and potential flows of an ideal fluid in the axisymmetric caseI. I. Vainshtein 109 The critical points of the Green's function of Laplace's equationA. Yanushauskas 123 Conservation laws and a priori estimates for certain nonlinear parabolic equationsS. I. Pokhozhaev 129 The Cauchy problem for the nonlinear Schrödinger equationA. V. Zhiber, A. B. Shabat 137 The Harnack inequality for generalized solutions of second order nonlinear $(k, 0)$-elliptic equationsL. P. Kuptsov 147 Weak solutions of second order quasilinear elliptic systemsG. N. Yakovlev 157 The $L_p$ summability of eigenfunction seriesSh. A. Alimov 164 The summability of Fourier series in a fundamental function system of Laplace's operator, in an arbitrary $N$-dimensional domain ($N\ge4$), by the $T_s(\alpha\lambda_k)$ methodG. I. Furletov 172 Short Communications A uniqueness condition of the Dirichlet problem for an equation of mixed type in a cylindrical domainA. M. Nakhushev 190 Methods of stating well-posed problems for second order linear hyperbolic equations on the planeA. M. Nakhushev 192 Certain problems of the type of the Cauchy problem for a certain degenerate equationV. A. Eleev 196 A certain mixed problem for the Tricomi equationV. I. Paškovskii 200 On the question of asymptotic stability of solutions of parabolic equationsÈ. N. Rudenko 204 The smoothness of solutions of the first boundary value problem for a degenerate elliptic equationV. N. Vragov 209