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 Partial Differential Equations Blow-up of solutions of a hyperbolic system: the critical caseD. Del Santo, E. Mitidieri 1155 Anisotropic Sobolev spaces and parabolic equations. I. SpacesA. Kalamayska, A. Milani 1162 Classification of positive solutions of the problem $\operatorname{div}(|\nabla u|^{p-2}\nabla u)+x\nabla(u^q)+\alpha u^q=0$ in $\mathbb R^n$G. Leoni 1170 Semilinear elliptic boundary value problems in resonance with superlinear nonlinearitiesT. Runst 1179 Integral Equations Boundary value problems and integral equations for some classes of pseudodifferential equations in nonsmooth domainsV. B. Vasil'ev (Vasilyev) 1186 Application of the method of boundary integral equations for determining the boundary-layer asymptotics of the solution of a nonlinear singularly perturbed boundary value problem of heat conduction in a two-layer domainV. F. Kravchenko, G. A. Nesenenko 1198 Linear integral equations of the second kind with a bi-Carleman kernel in the space $L^\infty$E. M. Kolodnaya, A. A. Kuleshov 1210 A mixed problem for the dissipative Helmholtz equation with an arbitrary partition of the boundaryP. A. Krutitskii 1216 On the admissibility of a pair $(Y,X)$ and asymptotics of the resolvent for a system of Volterra integral equationsZ. B. Tsalyuk 1226 On exact and approximate solutions of a system of singular integral equations with a Hilbert kernelM. A. Sheshko, D. S. Shulyaev 1231 Numerical methods Algorithms, optimal with respect to complexity, for the approximate solution of integral equationsI. V. Boykov 1240 A new approach to the solution of mixed boundary value problems for the Laplace and Helmholtz equationsYu. V. Gandel', I. K. Lifanov 1246 Justification of the generalized schemes of the $T$-matrix method on the basis of integral transformationsYu. A. Eremin 1254 On the well-posedness of a problem for solving a complete singular integral equationA. F. Matveev 1260 A discrete vortex method of increased accuracy for the numerical solution of a class of singular integral equationsJ. G. Sanikidze 1269 Approximate solution of convolution-type equations of the first kindN. Ya. Tikhonenko, E. A. Druzenko 1276 Short Communications On a first-order linear inhomogeneous equation with a singularityA. V. Glushak 1284 Finite hybrid Hankel integral transforms of the first kind (Fourier–Bessel– $\cdots$ –Bessel–Fourier)M. P. Lenyuk, V. V. Moroz 1286 On the solvability of elliptic boundary value problems on stratified setsO. M. Penkin, E. M. Bogatov, Yu. M. Kashkarov 1289 Direct methods for solving bisingular integral equations on Lyapunov skeletons in generalized Hölder spacesN. V. Snizhko 1291