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On movable singularities of self-similar solutions of semilinear wave equations

Radosław A. Kycia (2012)

Banach Center Publications

In this paper we analyze movable singularities of the solutions of the equation for self-similar profiles resulting from semilinear wave equation. We study local analytic solutions around two fixed singularity points of this equation- ρ = 0 and ρ = 1. The movable singularities of local analytic solutions at the origin will be connected with those of the Lane-Emden equation. The function describing approximately their position on the complex plane will be derived. For ρ > 1 some topological considerations...

On Newton's polygons, Gröbner bases and series expansions of perturbed polynomial programs

Konstantin Avrachenkov, Vladimir Ejov, Jerzy A. Filar (2006)

Banach Center Publications

In this note we consider a perturbed mathematical programming problem where both the objective and the constraint functions are polynomial in all underlying decision variables and in the perturbation parameter ε. Recently, the theory of Gröbner bases was used to show that solutions of the system of first order optimality conditions can be represented as Puiseux series in ε in a neighbourhood of ε = 0. In this paper we show that the determination of the branching order and the order of the pole (if...

On noncompact perturbation of nonconvex sweeping process

Myelkebir Aitalioubrahim (2012)

Commentationes Mathematicae Universitatis Carolinae

We prove a theorem on the existence of solutions of a first order functional differential inclusion governed by a class of nonconvex sweeping process with a noncompact perturbation.

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