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A family of new globally convergent linearization schemes for solving Richards' equation
ArticleAbstract: The Richards' equation models the water flow through porous media in groundwater aquifers and petrolPalabras claves:Degenerate nonlinear equations, Globally convergent schemes, Linearization schemes, Richards equationAutores:Ándres I. Ávila, Guillermo AlbujaFuentes:scopusA result on singularly perturbed elliptic problems
ArticleAbstract: We consider a class of equations of the form -ε2Δu + V(x)u = f(u), u ∈ H<sup>1</sup>(R<sup>N</sup>).Palabras claves:Singularly perturbed elliptic problems, Variational methodsAutores:Ándres I. Ávila, Jeanjean L.Fuentes:scopusA unified approach to symmetry for semilinear equations associated to the Laplacian in RN
ArticleAbstract: We show radial symmetry of positive solutions to the Hénon equation −Δu=|x|<sup>−ℓ</sup>u<sup>q</supPalabras claves:Entire solution, Maximum principle, Semi-linear elliptic equation, symmetryAutores:Ándres I. Ávila, Brock F.Fuentes:scopusStability results for the first eigenvalue of the Laplacian on domains in space forms
ArticleAbstract: We studied the two known works on stability for isoperimetric inequalities of the first eigenvalue oPalabras claves:Constant curvature, Faber-Krahn inequality, Space forms, Stability of eigenvalues, Szegö-Weinberger inequalityAutores:Ándres I. ÁvilaFuentes:scopusAsymptotics at infinity of solutions for p-Laplace equations in exterior domains
ArticleAbstract: Let 1 < p < N, and u be a nonnegative solution of - Δ<inf>p</inf> u = f (x, u) on R<sup>N</sup> {setPalabras claves:Asymptotics, Entire solution, Nonlinear elliptic equation, Nonlinear System, p-LaplaceAutores:Ándres I. Ávila, Brock F.Fuentes:scopusMultiple solutions of a coupled nonlinear Schrödinger system
ArticleAbstract: We will consider the relation between the number of positive standing waves solutions for a class ofPalabras claves:Elliptic system, Nehari manifold, Relative category, Schrödinger equation, Variational methodsAutores:Ándres I. Ávila, Wan Y.Fuentes:scopusMultiple solutions of nonlinear elliptic systems
ArticleAbstract: We proved a multiplicity result for a nonlinear elliptic system in R <sup>N</sup> . The functional rPalabras claves:Elliptic system, Indefinite, Multiple solutions, SemilinearAutores:Ándres I. Ávila, Yang J.Fuentes:scopusGlobal superlinear linearization schemes based on adaptive strategies for solving Richards’ equation
ArticleAbstract: The Richards’ equation is a nonlinear degenerate parabolic differential equation, whose numerical soPalabras claves:Adaptive linearization schemes, Degenerate nonlinear equations, Global convergence, Richards equation, Superlinear schemesAutores:Ándres I. Ávila, Guillermo Albuja, Miguel MurilloFuentes:scopusOn numerical methods for nonlinear singularly perturbed Schrödinger problems
ArticleAbstract: Nonlinear Schrödinger equations (NSE) model several important problems in Quantum Physics and MorphoPalabras claves:Dual weighted residual method, Patankar trick, Singularly perturbed Schrödinger problemsAutores:Ándres I. Ávila, Meister A., Steigemann M.Fuentes:scopusOn the existence and shape of least energy solutions for some elliptic systems
ArticleAbstract: We establish an existence result for strongly indefinite semilinear elliptic systems with Neumann boPalabras claves:Elliptic system, Indefinite, Positive solutions, SemilinearAutores:Ándres I. Ávila, Yang J.Fuentes:scopus