This monograph presents extensions of the MoserBangert approach that include solutions of a family of nonlinear elliptic PDEs on Rn and an AllenCahn PDE model of phase transitions. After recalling the relevant MoserBangert results, Extensions of MoserBangert Theory pursues the rich structure of the set of solutions of a simpler model case, expanding upon the studies of Moser and Bangert to include solutions that merely have local minimality properties. Subsequent chapters build upon the introductory results, making the monograph self contained.The work is intended for mathematicians who specialize in partial differential equations and may also be used as a text for a graduate topics course in PDEs.

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