LEADER 03373nam 2200637 450 001 996466375703316 005 20220323173054.0 010 $a3-540-48099-4 024 7 $a10.1007/BFb0073859 035 $a(CKB)1000000000437160 035 $a(SSID)ssj0000327315 035 $a(PQKBManifestationID)12124369 035 $a(PQKBTitleCode)TC0000327315 035 $a(PQKBWorkID)10301352 035 $a(PQKB)10967694 035 $a(DE-He213)978-3-540-48099-0 035 $a(MiAaPQ)EBC5578553 035 $a(Au-PeEL)EBL5578553 035 $a(OCoLC)1066199680 035 $a(MiAaPQ)EBC6842927 035 $a(Au-PeEL)EBL6842927 035 $a(OCoLC)1292362898 035 $a(PPN)155206524 035 $a(EXLCZ)991000000000437160 100 $a20220303d1993 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aTopological methods for variational problems with symmetries /$fThomas Bartsch 205 $a1st ed. 1993. 210 1$aBerlin ;$aHeidelberg :$cSpringer-Verlag,$d[1993] 210 4$dİ1993 215 $a1 online resource (X, 158 p.) 225 1 $aLecture Notes in Mathematics ;$v1560 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-57378-X 327 $aCategory, 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. 330 $aSymmetry has a strong impact on the number and shape of solutions to variational problems. This has been observed, for instance, in the search for periodic solutions of Hamiltonian systems or of the nonlinear wave equation; when one is interested in elliptic equations on symmetric domains or in the corresponding semiflows; and when one is looking for "special" solutions of these problems. This book is concerned with Lusternik-Schnirelmann theory and Morse-Conley theory for group invariant functionals. These topological methods are developed in detail with new calculations of the equivariant Lusternik-Schnirelmann category and versions of the Borsuk-Ulam theorem for very general classes of symmetry groups. The Morse-Conley theory is applied to bifurcation problems, in particular to the bifurcation of steady states and hetero-clinic orbits of O(3)-symmetric flows; and to the existence of periodic solutions nearequilibria of symmetric Hamiltonian systems. Some familiarity with the usualminimax theory and basic algebraic topology is assumed. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1560. 606 $aCalculus of variations 606 $aSymmetry groups 606 $aCritical point theory (Mathematical analysis) 615 0$aCalculus of variations. 615 0$aSymmetry groups. 615 0$aCritical point theory (Mathematical analysis) 676 $a515.64 700 $aBartsch$b Thomas$f1958-$060120 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466375703316 996 $aTopological methods for variational problems with symmetries$978641 997 $aUNISA