[en] Using the Leray-Schauder continuation principle we give some existence results for the Picard boundary value problem of second order asymptotically homogeneous equations. Some previous results by Tippett, Gaines-Mawhin, Lazer-Leach will be extended.

[en] In this paper, we study solvability of one boundary value problem for a nonlocal analogue of mixed parabolic-hyperbolic fractional-order equation with involution and degeneration. The problem is solved by using the variable separation method. Theorems on existence and uniqueness of solution to the considered problem are proved. Stability of solution to the considered problem is also established with respect to the nonlocal condition.

[en] ADI (Alternating Direction Implicit) iteration has been used to solve a variety of discretized boundary value problems. Rapid convergence and rigorous mathematical foundations have been established for certain model problems. The application has been broadened by the use of model problem ADI preconditioning for the solution of more general problems. When the spectra of the two matrices appearing in the iteration equations differ, the choice of optimum iteration parameters and associated rate of convergence for the resulting two-variable problem must be addressed. W.B. Jordan reduced the real two-variable minimax problem to a one variable problem by means of a linear fractional transformation. His result was achieved with considerable algebra which was never published. An alternative approach which reduces the algebra and yields the transformation parameters in a simpler form is described here. (Author)

[en] Some new results on the existence of multiple solutions for asymptotically linear elliptic boundary value problems via critical groups are obtained. (author). 11 refs

[en] We study the solvability of linear inverse problems for ultraparabolic equations with an unknown coefficient depending only on the spatial variables. The feature of such problems is special overdetermination conditions. We use the method based on reducing the inverse problem to a nonlocal boundary-value problem for ultraparabolic equations.

[en] An evident matrix two-channel representation for system hamiltonians with internal structure, obtained within the framework of symmetric operator extention theory is found. Generalized potentials are constructed which are equivalent to the zero radius interaction with internal structure and reproduce automatically the respective boundary conditions. 26 refs

[en] In this paper we prove identifiability and stability estimates for a local-data inverse boundary value problem for a magnetic Schrödinger operator in dimension $n⩾<!--\; ???\; -->3$. We assume that the inaccessible part of the boundary is part of a hyperplane. We improve the identifiability result obtained by Krupchyk et al (2012 Commun. Math. 313 87–126) and also derive the corresponding stability estimates. We obtain $\log$-estimates for magnetic and electric potentials. (paper)

[en] We state solvability conditions for a multipoint boundary-value problem for linear second-order functional-differential equation.

[en] We study a resonant functional boundary value problem of fractional order. Our results are based on the coincidence degree theory of Mawhin and improve those in a recent paper of Y. Zou and Y. Cui [Adv. Difference Equ. 2013 (2013), 1–25].

[en] We study boundary properties of polyharmonic functions. In particular, a criterion is obtained (in terms of the radial growth of the derivative) for the existence a.e. of angular boundary values for a polyharmonic function bounded in the unit ball.