Cabada Fernández, AlbertoSaavedra López, Lorena2018-02-232018-02-232017http://hdl.handle.net/10347/16505This Thesis contains a detailed collection of the different results proved by the author in her predoctoral stage. The interest of the non-linear differential equations is well-known. This is due to their applications in different fields, such as physics, economy, medicine, biology or chemistry. It is very important to make a precise study of the existence of solutions for this kind of problems, as well as their uniqueness or multiplicity. We focus on the qualitative analysis of diverse boundary value problems, both linear and non-linear ones. Indeed, in most of the cases, our aim is to prove the existence of constant sign solutions in their definition interval. This interest comes from the constant sign of many of the magnitudes which are modelled by this kind of problems.engEsta obra atópase baixo unha licenza internacional Creative Commons BY-NC-ND 4.0. Calquera forma de reprodución, distribución, comunicación pública ou transformación desta obra non incluída na licenza Creative Commons BY-NC-ND 4.0 só pode ser realizada coa autorización expresa dos titulares, salvo excepción prevista pola lei. Pode acceder Vde. ao texto completo da licenza nesta ligazón: https://creativecommons.org/licenses/by-nc-nd/4.0/deed.glhttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.glboundary value problemsGreen's functionsconstant sign solutionsspectral theoryMaterias::Investigación::12 Matemáticas::1202 Análisis y análisis funcional::120219 Ecuaciones diferenciales ordinariasMaterias::Investigación::12 Matemáticas::1202 Análisis y análisis funcional::120201 Algebra de operadoresdoctoral thesisopen access