Computer-assisted Multiplicity Proofs for Emden's Equation on Domains with Hole

In this thesis we consider Emden's equation on a parameter dependent domain with hole and describe a computer-assisted method for proving existence and multiplicity of solutions to that problem. We obtain results for discrete parameter values as well as for some parameter intervals, in which case also the existence of smooth solution branches is proved. Moreover we prove the existence of a one-bump solution to Emden's equation on an unbounded L-shaped domain.