03373nam 2200637 450 99646637570331620220323173054.03-540-48099-410.1007/BFb0073859(CKB)1000000000437160(SSID)ssj0000327315(PQKBManifestationID)12124369(PQKBTitleCode)TC0000327315(PQKBWorkID)10301352(PQKB)10967694(DE-He213)978-3-540-48099-0(MiAaPQ)EBC5578553(Au-PeEL)EBL5578553(OCoLC)1066199680(MiAaPQ)EBC6842927(Au-PeEL)EBL6842927(OCoLC)1292362898(PPN)155206524(EXLCZ)99100000000043716020220303d1993 uy 0engurnn#008mamaatxtccrTopological methods for variational problems with symmetries /Thomas Bartsch1st ed. 1993.Berlin ;Heidelberg :Springer-Verlag,[1993]©19931 online resource (X, 158 p.)Lecture Notes in Mathematics ;1560Bibliographic Level Mode of Issuance: Monograph3-540-57378-X Category, genus and critical point theory with symmetries -- Category and genus of infinite-dimensional representation spheres -- The length of G-spaces -- The length of representation spheres -- The length and Conley index theory -- The exit-length -- Bifurcation for O(3)-equivariant problems -- Multiple periodic solutions near equilibria of symmetric Hamiltonian systems.Symmetry has a strong impact on the number and shape of solutions to variational problems. This has been observed, for instance, in the search for periodic solutions of Hamiltonian systems or of the nonlinear wave equation; when one is interested in elliptic equations on symmetric domains or in the corresponding semiflows; and when one is looking for "special" solutions of these problems. This book is concerned with Lusternik-Schnirelmann theory and Morse-Conley theory for group invariant functionals. These topological methods are developed in detail with new calculations of the equivariant Lusternik-Schnirelmann category and versions of the Borsuk-Ulam theorem for very general classes of symmetry groups. The Morse-Conley theory is applied to bifurcation problems, in particular to the bifurcation of steady states and hetero-clinic orbits of O(3)-symmetric flows; and to the existence of periodic solutions nearequilibria of symmetric Hamiltonian systems. Some familiarity with the usualminimax theory and basic algebraic topology is assumed.Lecture notes in mathematics (Springer-Verlag) ;1560.Calculus of variationsSymmetry groupsCritical point theory (Mathematical analysis)Calculus of variations.Symmetry groups.Critical point theory (Mathematical analysis)515.64Bartsch Thomas1958-60120MiAaPQMiAaPQMiAaPQBOOK996466375703316Topological methods for variational problems with symmetries78641UNISA