Abstract:
n this thesis some Lane-Emden problems of different order are studied. Tackling the issue of existence of a positive solution and regularity of the solutions are of paramount importance for each instance. In addition to discussing the general Lane-Emden equation, the cases of having an advection term to the original problem and investigating some fourth order nonlinear Dirichlet and Navier problems are of considerable interest. While the well-studied general equation points out that for p≥N+2/N−2 and Ω a star-shaped domain in RN there would be no non-trivial solution, some advantageous results regarding the existence of a positive solution and regularity of the solutions on a general bounded domain inRNare addressed for the equations where an advection is involved, as well as some nonlinear fourth order problem with given Dirichlet and Navier boundary conditions.
