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This unique book focuses on critical point theory for strongly indefinite functionals in order to deal with nonlinear variational problems in areas such as physics, mechanics and economics. With the original ingredients of Lipschitz partitions of unity of gage spaces (nonmetrizable spaces), Lipschitz normality, and sufficient conditions for the normality, as well as existence-uniqueness of flow of ODE on gage spaces, the book presents for the first time a deformation theory in locally convex topological vector spaces. It also offers satisfying variational settings for homoclinic-type solutions

Calculus of variations. --- Diophantine equations. --- Diophantic equations --- Equations, Diophantic --- Equations, Diophantine --- Equations, Indefinite --- Equations, Indeterminate --- Indefinite equations --- Indeterminate equations --- Diophantine analysis --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima