DAM - Artículos
http://hdl.handle.net/10481/31358
2020-05-31T07:57:19ZPulse Processes in Networks and Evolution Algebras
http://hdl.handle.net/10481/61798
Pulse Processes in Networks and Evolution Algebras
Becerra Guerrero, Julio Antonio; Beltrán, María; Velasco Collado, María Victoria
In this paper, we merge two theories: that of pulse processes on weighted digraphs and
that of evolution algebras. We enrich both of them. In fact, we obtain new results in the theory of
pulse processes thanks to the new algebraic tool that we introduce in its framework, also extending
the theory of evolution algebras, as well as its applications.
A singularity as a break point for the multiplicity of solutions to quasilinear elliptic problems
http://hdl.handle.net/10481/60245
A singularity as a break point for the multiplicity of solutions to quasilinear elliptic problems
López Martínez, Salvador
We study a boundary value elliptic problem having a lower order nonlinear term with subquadratic growth in the gradient of the solution and possibly singular when the solution vanishes. If the singularity is mild enough (and even in the absence of the singularity), we prove an existence and multiplicity result. On the contrary, we prove an existence and uniqueness result for strong singularities.
The Gelfand problem for the 1-homogeneous p-Laplacian
http://hdl.handle.net/10481/59925
The Gelfand problem for the 1-homogeneous p-Laplacian
Carmona Tapia, José; Molino Salas, Alexis; Rossi, Julio D.
In this paper, we study the existence of viscosity solutions to the Gelfand problem for the 1-homogeneous
p-Laplacian in a bounded domain Ω ⊂ ℝN, that is, we deal with
− 1
p − 1|∇u|2−p div(|∇u|p−2∇u) = λeu
in Ω with u = 0 on ∂Ω. For this problem we show that, for p ∈ [2, ∞], there exists a positive critical value
λ∗ = λ∗(Ω, N, p) such that the following holds:
∙ If λ < λ∗, the problem admits a minimal positive solution wλ.
∙ If λ > λ∗, the problem admits no solution.
Moreover, the branch of minimal solutions {wλ} is increasing with λ. In addition, using degree theory, for
fixed p we show that there exists an unbounded continuum of solutions that emanates from the trivial solution
u = 0 with λ = 0, and for a small fixed λ we also obtain a continuum of solutions with p ∈ [2, ∞].
Analytic aspects of evolution algebras
http://hdl.handle.net/10481/59808
Analytic aspects of evolution algebras
Mellon, P.; Velasco Collado, María Victoria
We prove that every evolution algebra A is a normed algebra, for an l1-norm defined in terms of a fixed natural basis. We further show that a normed evolution algebra A is a Banach algebra if and only if A=A1⊕A0, where A1 is finite-dimensional and A0 is a zero-product algebra. In particular, every nondegenerate Banach evolution algebra must be finite-dimensional and the completion of a normed evolution algebra is therefore not, in general, an evolution algebra. We establish a sufficient condition for continuity of the evolution operator LB of A with respect to a natural basis B, and we show that LB need not be continuous. Moreover, if A is finite-dimensional and B={e1,…,en}, then LB is given by Le, where e=∑iei and La is the multiplication operator La(b)=ab, for b∈A. We establish necessary and sufficient conditions for convergence of (Lna(b))n, for all b∈A, in terms of the multiplicative spectrum σm(a) of a. Namely, (Lna(b))n converges, for all b∈A, if and only if σm(a)⊆Δ∪{1} and ν(1,a)≤1, where ν(1,a) denotes the index of 1 in the spectrum of La.
Weak-2-local isometries on uniform algebras and Lipschitz algebras
http://hdl.handle.net/10481/59468
Weak-2-local isometries on uniform algebras and Lipschitz algebras
Li, Lei; Peralta Pereira, Antonio Miguel; Wang, Liguang; Wang, Ya-Shu
We establish spherical variants of the Gleason-Kahane-Zelazko and
Kowalski-Slodkowski theorems, and we apply them to prove that every weak-2-local
isometry between two uniform algebras is a linear map. Among the consequences,
we solve a couple of problems posed by O. Hatori, T. Miura, H. Oka, and H. Takagi
in 2007.