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Title: | Positive radial solutions for quasilinear equations = Soluciones radiales positivas para ecuaciones cuasilineales. |
Other Titles: | Soluciones radiales positivas para ecuaciones cuasilineales. |
Authors: | Mahadevan, Rajesh; supervisor de grado Lorca, Sebastián; supervisor de grado Guajardo Bravo, Juan Carlos |
Keywords: | Teoría de Punto Fijo;Bases de Schauder;Análisis Funcional |
Issue Date: | 2020 |
Publisher: | Universidad de Concepción. |
Abstract: | The study of existence, multiplicity and non-existence of positive solutions to semi-linear and quasi-linear elliptic equations is relevant to many applications ranging from thermal iginition of gases [14], quantum field theory and statistical mehcanics [7], gravitational equilibrium of stars [19] etc. This work aims to study the existence, multiplicity and no-existence of positive radial solutions(other than the 0 solution) to the problem div(A(|∇u|)∇u) + λk(|x|)f(u) = 0, x ∈ Ω. (1.0.1) in symmetric exterior domains Ω ⊂ R n (complements of balls centered at the origin) for n ≥ 2. The non negative functions A, k and f satisfy certain properties that we will specify later and λ > 0 is a parameter. The class of functions A which we consider will include A(|p|) = |p| m−2 , m > 1 associated to the m-laplacian operator div (|∇u| m−2∇u) (non linear if m 6= 2 and coincides with the Laplacian for m = 2) applicable to diffusion problems. The class will also include slight perturbations . |
Description: | Tesis para optar al grado de Doctor en Matemática. |
URI: | http://repositorio.udec.cl/jspui/handle/11594/4643 |
Appears in Collections: | Matemática - Tesis Doctorado |
Files in This Item:
File | Description | Size | Format | |
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Tesis Soluciones radiales positivas para ecuaciones cuasilineales.Image.Marked.pdf | 552,55 kB | Adobe PDF | View/Open |
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