En el presente trabajo presentamos el Espectro de Fucik del operador Laplaciano -∆ bajo condiciones de frontera tipo Dirichlei sobre un dominio Ω regular acotado en Rn, se demuestra el comportamiento asintótico de la primera curva contenida en él y se brinda una descripción completa del Espectro de Fucik para el caso n = 1.

In this paper, we prove that the solution of nonlinear Ordinary Differential Equations (ODE), with continuous coefficients and non-linear terms tending to zero at infinity, have an asymptotic behavior similar to the solution of there corresponding linear equations.

In this paper we developed conditions for orthogonality of polynomial Solutions of the fourth order differential equations with polynomial coefficients. Also, we present the fourth order equations with Legendre polynomials, Laguerre polynomials and Hermite polynomials solutions.

In this article, we consider the Fučik equation in Ω = < 0, π > with Sturm-Liouville boundary conditions. We obtain its Fučik spectrum also the complete description and properties of the curves on it.

In this work, the Fucik Spectrum for the boundary value problemis studied, and the Fucik curves contained in this spectrum are described.

In this work we study the Fucik spectrum for the following system of secondorder ordinary differential equationswhere Bu = 0 represents the Dirichlet or Newmann type boundary conditions. We study the case in which the nontrivial solutions (u,v) of the problem, keep their sign in the whole interval (0,1) and we prove: the Fucik spectrum for the Dirichlet problem is the union of a plane with an hyperbolic cylinder, while for the Newmann problem, the Fucik spectrum is formed by the Cartesian planes. 

En este trabajo mostramos algunas propiedades de las soluciones no triviales del sistema acoplado ...

En el presente trabajo presentamos el Espectro de Fucik del operador Laplaciano -∆ bajo condiciones de frontera tipo Dirichlei sobre un dominio Ω regular acotado en Rn, se demuestra el comportamiento asintótico de la primera curva contenida en él y se brinda una descripción completa del Espectro de Fucik para el caso n = 1.

In this paper, we prove that the solution of nonlinear Ordinary Differential Equations (ODE), with continuous coefficients and non-linear terms tending to zero at infinity, have an asymptotic behavior similar to the solution of there corresponding linear equations.

Se proporciona las condiciones para la ortogonalidad de soluciones polinomiales de ecuaciones diferenciales de cuarto orden con coeficientes polinomiales. Adicionalmente, se presenta una clase de este tipo de ecuaciones cuyas soluciones son los polinomios de Legendre, Laguerre y Hermite.

En este trabajo consideramos la ecuación de fučik en Ω = < 0, π  > con condiciones de  frontera Sturm-Liouville. Obtenemos su espectro de Fučik, así como la descripción completa y las propiedades de las curvas contenidas en él

En este trabajo se estudia el Espectro de Fucik para el problema de valor frontera ... y se describen las curvas de Fucik contenidas en dicho espectro.

En este trabajo se estudia el espectro de Fucik para el siguiente sistema deecuaciones diferenciales ordinarias de segundo orden ...donde Bu = 0 representa las condiciones de frontera tipo Dirichlet o tipo Newmann. Se estudia el caso en que las soluciones no triviales (u, v) del problema, conservan su signo en todo el intervalo (0,1) Y se obtiene como resultado que para el problema tipo Dirichlet, el espectro de Fucik está formado por la unión de un plano y un cilindro hiperbólico, mientras que para el problema tipo Newmann el espectro está formado por los planos cartesianos.

En este trabajo mostramos algunas propiedades de las soluciones no triviales del sistema acoplado ...

Estudia el Espectro de Fucik para un sistema acoplado de ecuaciones diferenciales ordinarias con valores en la frontera, donde λ+, λ−, μ− ∈ R+ ∪{0} , w+ = max{w, 0 } , w− = max{−w, 0 } y Bw = 0 representa las condiciones de frontera tipo Dirichlet o Neumann. Obtiene familias explícitas de puntos (λ+, λ−, μ−) del espectro de Fucik y construye familias explícitas de soluciones no triviales (u, v) para el problema dado. Demuestra que el espectro de Fucik está formado por superficies y describe explícitamente la parte trivial del espectro, correspondiente a soluciones que no cambian de signo, probando que para el problema Dirichlet está compuesto por un plano y un cilindro hiperbólico, y para el problema Neumann está compuesto por los tres planos coordenados. Luego, usando el Teorema de la Función Implícita, prueba la existencia de superficies en la parte no tr...

In this article we prove that the Cauchy problem associated to the heat equation in periodic Sobolev spaces is well posed. We do this in an intuitive way using Fourier theory and in a fine version using Semigroups theory, inspired by works Iorio [1] and Santiago and Rojas [3]. Also, we study the relationship between the initial data and differentiability of the solution.Finally, we study the corresponding nonhomogeneous problem and prove it is locally well posed and even more we obtain the continuous dependence of the solution with respect to the initial data and the non homogeneity.

In this article, we first prove that the initial value problem associated to the homogeneous wave equation in periodic Sobolev spaces has a global solution and the solution has continuous dependence with respect to the initial data, in [0; T], T > 0. We do this in an intuitive way using Fourier theory and in a fine version introducing families of strongly continuous operators, inspired by the works of Iorio [4] and Santiago and Rojas [7].Also, we prove that the energy associated to the wave equation is conservative in intervals [0; T], T > 0.As a final result, we prove that the initial value problem associated to the non homogeneous wave equation has a local solution and the solution has continuous dependence with respect to the initial data and the non homogeneous part of the problem.

In this article, we prove the uniqueness solution of the homogeneous and non-homogeneous heat equation in periodic Sobolev spaces. We do it in a different way from what we did in [3], in this case we perform differential calculus in Hs-per and we take advantage of the immersion and properties of periodic Sobolev spaces. With this proof we gain to visualize the dissipative property of the homogeneous problem and with this we deduce the continuous dependence with respect to the initial data and the uniqueness solution for both cases: homogeneous and non-homogeneous.

In this article we prove that the Cauchy problem associated to the heat equation in periodic Sobolev spaces is well posed. We do this in an intuitive way using Fourier theory and in a fine version using Semigroups theory, inspired by works Iorio [1] and Santiago and Rojas [3]. Also, we study the relationship between the initial data and differentiability of the solution.Finally, we study the corresponding nonhomogeneous problem and prove it is locally well posed and even more we obtain the continuous dependence of the solution with respect to the initial data and the non homogeneity.

In this article, we first prove that the initial value problem associated to the homogeneous wave equation in periodic Sobolev spaces has a global solution and the solution has continuous dependence with respect to the initial data, in [0; T], T > 0. We do this in an intuitive way using Fourier theory and in a fine version introducing families of strongly continuous operators, inspired by the works of Iorio [4] and Santiago and Rojas [7].Also, we prove that the energy associated to the wave equation is conservative in intervals [0; T], T > 0.As a final result, we prove that the initial value problem associated to the non homogeneous wave equation has a local solution and the solution has continuous dependence with respect to the initial data and the non homogeneous part of the problem.