Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> vol. 21 num. 3 lang. es <![CDATA[SciELO Logo]]> <![CDATA[PERIODIC STRONG SOLUTIONS OF THE MAGNETOHYDRODYNAMIC TYPE EQUATIONS]]> We obtain, using the spectral Galerkin method together with compactness arguments, existence and uniqueness of periodic strong solu-tions for the magnetohydrodynamic type equations <![CDATA[THE HOMOTOPY TYPE OF INVARIANT CONTROL SET]]> Let G be a noncompact semi-simple Lie group, consider S a semi-group which contains a large Lie semigroup. We computer the homo-topy type pin(C), where C is the invariant control set of the homoge-neous space G=P with P <FONT FACE=Symbol>Ì</FONT> G a parabolic subgroup of G <![CDATA[WEIGHTED HOMOGENEOUS MAP GERMS OF CORANK ONE FROM C <SUP>3</SUP> TO C <SUP>3</SUP> AND POLAR MULTIPLICITIES]]> For quasi-homogeneous and finitely determined corank one map germs f : (C ³ ; 0) -> (C ³ ; 0) we obtain formulae in function of the degree and weight of f for invariantes on the stable types of f, as polar multiplicities, number of Milnor, number of Lê. We minimize also the number of invariantes for 7, to resolve the problem that decides the Whitney equisingularity of families of such maps germs. To finalize use these formulae to increase the list of invariants of some normal forms of f <![CDATA[CRITICAL POINT THEOREMS AND APPLICATIONS]]> We Consider the nonlinear Dirichlet problem: <IMG SRC="http:/fbpe/img/proy/v21n3/img04-01.gif" WIDTH=350 HEIGHT=56> where . omega <FONT FACE=Symbol>Î</FONT> R N is a bounded open domain, F : omega chi R -> R is a carath´eodory function and DuF(x; u) is the partial derivative of F. We are interested in the resolution of problem (1) when F is concave. Our tool is absolutely variational. Therefore, we state and prove a critical point theorem which generalizes many other results in the literature and leads to the resolution of problem (1). Our theorem allows us to express our assumptions on the nonlinearity in terms of F and not of <FONT FACE=Symbol>Ñ</FONT>F. Also, we note that our theorem doesn’t necessitate the verification of the famous compactness condition introduced by Palais-Smale or any of its variants <![CDATA[<I>JORDAN NILALGEBRAS OF DIMENSION 6</I>]]> It is known the classification of commutative power-associative nilalgebras of dimension <FONT FACE=Symbol>&pound;</FONT>4 (see, [4]). In [2], we give a description of commutative power-associative nilalgebras of dimension 5. In this work we describe Jordan nilalgebras of dimension 6