Mahadevan, RajeshLorca, SebastiánGuajardo Bravo, Juan Carlos2021-03-052024-05-152024-08-282021-03-052024-05-152024-08-282020https://repositorio.udec.cl/handle/11594/4643Tesis presentada para optar al grado de Doctor en Matemática.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 .enCC BY-NC-ND 4.0 DEED Attribution-NonCommercial-NoDerivs 4.0 InternationalTeoría de Punto FijoBases de SchauderAnálisis FuncionalTesis