Valdebenito Castillo, Dario2018-07-262018-07-262017-07https://hdl.handle.net/11299/198410University of Minnesota Ph.D. dissertation. July 2017. Major: Mathematics. Advisor: Peter Polacik. 1 computer file (PDF); iv, 106 pages.We consider semilinear equations on the N+1-dimensional space. We give sufficient conditions for the existence of solutions which are quasiperiodic in one variable and decaying in the others. Such solutions are found using a center manifold reduction and results from the KAM theory. We discuss several classes of nonlinearities to which our results apply.enCenter manifoldElliptic equationsEntire solutionsKAM theoremNemytskii operators on Sobolev spacesQuasiperiodic solutionsThesis or Dissertation