Journal of Nonlinear Mathematical Physics

Volume 8, Issue 1, February 2001
Pages: 8 - 30
In this paper we study homogenization of quasi-linear partial differential equations of the form -div (a (x, x/h, Duh)) = fh on with Dirichlet boundary conditions. Here the sequence (h) tends to 0 as h and the map a (x, y, ) is periodic in y, monotone in and satisfies suitable continuity conditions....
Pages: 54 - 58
I propose an orthogonalization procedure preserving the grading of the initial graded set of linearly independent vectors. In particular, this procedure is applicable for orthonormalization of any countable set of polynomials in several (finitely many) ideterminates.
Pages: 59 - 64
A depending on a complex parameter k superanalog SL of Calogero operator is costructed; it is related with the root system of the Lie superalgebra gl(n|m). For m = 0 we obtain the usual Calogero operator; for m = 1 we obtain, up to a change of indterminates and parameter k the operator constructed by...
Pages: 65 - 95
A special asymptotic solution of the Painlevé-2 equation with small parameter is stdied. This solution has a critical point t corresponding to a bifurcation phenomenon. When t < t the constructed solution varies slowly and when t > t the solution oscillates very fast. We investigate the transitional...