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- W3188820890 abstract "A classical nonlinear equation on a complete Riemannian manifold is considered. The existence of solutions connecting any two points is studied, i.e., for > 0 the critical points of the functional with (0) = , () = . When the potential has a subquadratic growth with respect to x, admits a minimum critical point for any > 0 (infinitely many critical points if the topology of is not trivial). When has an at most quadratic growth, i.e., , this property does not hold, but an optimal arrival time () > 0 exists such that, if 0 < < (), any pair of points in can be joined by a critical point of the corresponding functional. For the existence and multiplicity results, variational methods and Ljusternik-Schnirelman theory are used. The optimal value is fulfilled by the harmonic oscillator. These ideas work for other related problems." @default.
- W3188820890 created "2021-08-16" @default.
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- W3188820890 date "2003-02-01" @default.
- W3188820890 modified "2023-10-16" @default.
- W3188820890 title "A Quadratic Bolza—Type Problem in a Riemannian Manifold" @default.
- W3188820890 hasPublicationYear "2003" @default.
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