The convergence behaviour is investigated of solution algorithms for the anisotropic Poisson problem on partially ordered, sparse families of regular grids in 3D. In order to study multilevel techniques on sparse families of grids, first we consider the convergence of a two-level algorithm that applies semi-coarsening successively in each of the coordinate directions. This algorithm shows good ...

We study the growth of solutions of higher order complex differential equations in an angular domain of the unit disc instead of the whole unit disc. Some conditions on coefficient functions, which will guarantee all non-trivial solutions of the higher order differential equations have fast growing, are found in this paper. AMS (2010) Mathematics Subject Classification: 34M10, 30D35

In this paper, we study one-dimensional Newtonian filtration equation including unbounded sources with multiple delays. The existence of nonnegative non-trivial time periodic solutions will be established by the Leray-Schauder fixed point theorem based on some suitable Lyapunov functionals and some a priori estimates for all possible periodic solutions.

We give a correspondence between non-trivial solutions to a parametric family of cubic Thue equations X − mXY − (m + 3)XY 2 − Y 3 = k where k | m+3m+9 and isomorphic simplest cubic fields. By applying R. Okazaki’s result for isomorphic simplest cubic fields, we obtain all solutions to the family of cubic Thue equations for k | m + 3m + 9.

Classical vacuum pure gauge solutions of Euclidean two-dimensional SU(2) Yang–Mills theories are studied. Topologically non-trivial vacua are found in a class of gauge group elements isomorphic to S2. These solutions are unexpectedly related to the solution of the non-linear O(3) model and to the motion of a particle in a periodic potential. PACS: 11.10.Kk, 11.10.Lm. () On leave of absence from...

In this article, we study the existence of non-trivial subnormal solutions for second-order linear differential equations. We show that under certain conditions some differential equations do not have subnormal solutions, also that the hyper-order of every solution equals one.

In this paper we deal with the study of limits of solutions of a class of fully nonlinear elliptic problems at nearly critical growth. By means of P.L. Lions’ concentrationcompactness principle, we prove an alternative result for the existence of non-trivial solutions of the limit problem.

We show that for all integers m and n there are no non-trivial solutions of Thue equation x − 2mnxy + 2 ( m − n + 1 ) xy + 2mnxy + y = 1, satisfying the additional condition gcd(xy,mn) = 1.

It is shown that in 5D Kaluza-Klein theory there are everywhere regular wormhole-like solutions in which the magnetic field at the center is the origin of a rotation on the peripheral part of these solutions. The time on the peripheral part is topologically non-trivial and magnetic field is suppressed in comparison with the electric one.