Isbn: 9780817636555 - periodic solutions of singular lagrangian systems: 10 (16 risultati)

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Condizione: New. A summary and synthesis of recent research demonstrating that variational methods can be used to successfully handle systems with singular potential, the Lagrangian systems. The classic cases of the Kepler problem and the N-body problem are used as specific examples. Series: Progress in Nonlinear Differential Equations and Their Applications. Num Pages: 172 pages, biography. BIC Classification: PBK. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 234 x 156 x 11. Weight in Grams: 426. . 1993. Hardback. . . . . …

Buch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - Thismonographdealswiththeexistenceofperiodicmotionsof Lagrangiansystemswith ndegreesoffreedom ij + V'(q) =0, where Visasingularpotential.Aprototypeofsuchaproblem, evenifitisnottheonlyphysicallyinterestingone,istheKepler problem . q 0 q+yqr= . This,jointlywiththemoregeneralN-bodyproblem,hasalways beentheobjectofagreatdealofresearch.Mostofthoseresults arebasedonperturbationmethods,andmakeuseofthespecific featuresoftheKeplerpotential. OurapproachismoreonthelinesofNonlinearFunctional Analysis:ourmainpurposeistogiveafunctionalframefor systemswithsingularpotentials,includingtheKeplerandthe N-bodyproblemasparticularcases.PreciselyweuseCritical PointTheorytoobtainexistenceresults,qualitativeinnature, whichholdtrueforbroadclassesofpotentials.Thishighlights thatthevariationalmethods,whichhavebeenemployedtoob tainimportantadvancesinthestudyofregularHamiltonian systems,canbesuccessfallyusedtohandlesingularpotentials aswell. Theresearchonthistopicisstillinevolution,andtherefore theresultswewillpresentarenottobeintendedasthefinal ones. Indeedamajorpurposeofourdiscussionistopresent methodsandtoolswhichhavebeenusedinstudyingsuchprob lems. Vlll PREFACE Partofthematerialofthisvolumehasbeenpresentedina seriesoflecturesgivenbytheauthorsatSISSA,Trieste,whom wewouldliketothankfortheirhospitalityandsupport. We wishalsotothankUgoBessi,PaoloCaldiroli,FabioGiannoni, LouisJeanjean,LorenzoPisani,EnricoSerra,KazunakaTanaka, EnzoVitillaroforhelpfulsuggestions. May26,1993 Notation n 1.For x, yE IR , x. ydenotestheEuclideanScalarproduct, and IxltheEuclideannorm. 2. meas(A)denotestheLebesguemeasureofthesubset Aof n IR 3.Wedenoteby ST =[0,T]/{a,T}theunitarycirclepara metrizedby t E[0,T].Wewillalsowrite SI= ST=I. n 1 n 4.Wewillwrite sn = {xE IR + : Ixl =I}andn = IR {O}. n 5.Wedenoteby LP([O,T], IR ),1~ p~+00,theLebesgue spaces,equippedwiththestandardnorm lIulip. l n l n 6. H (ST, IR )denotestheSobolevspaceof u E H ,2(0, T; IR ) suchthat u(O) = u(T).Thenormin HIwillbedenoted by lIull2 = lIull~ + lIull~ 7.Wedenoteby( 1 )and11 11respectivelythescalarproduct andthenormoftheHilbertspace E. 8.For uE E, EHilbertorBanachspace,wedenotetheball ofcenter uandradiusrby B(u,r) = {vE E: lIu- vii~ r}.Wewillalsowrite B = B(O, r). r 1 1 9.WesetA (n) = {uE H (St,n)}. k 10.For VE C (1Rxil,IR)wedenoteby V'(t, x)thegradient of Vwithrespectto x. l 11.Given f E C (M,IR), MHilbertmanifold,welet r = {uEM: f(u) ~ a}, f-l(a,b) = {uE E : a~ f(u) ~ b}. x NOTATION 12.Given f E C1(M,JR), MHilbertmanifold,wewilldenote by Zthesetofcriticalpointsof fon Mandby Zctheset Z U f-l(c, c). 13.Givenasequence UnE E, EHilbertspace,by Un ---'' Uwe willmeanthatthesequence Unconvergesweaklyto u. 14.With Pds. (E)wewilldenotethesetoflinearandcontinuous operatorson E. 15.With Ck''''(A,JR)wewilldenotethesetoffunctions ffrom AtoJR, ktimesdifferentiablewhosek-derivativeisHolder continuousofexponent0. Main Assumptions Wecollecthere,forthereader'sconvenience,themainassump tionsonthepotential Vusedthroughoutthebook. (VO) VEC1(lRXO,lR),V(t+T,x)=V(t,X) V(t,x)ElRXO, (VI) V(t,x).…

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Condizione: New. A summary and synthesis of recent research demonstrating that variational methods can be used to successfully handle systems with singular potential, the Lagrangian systems. The classic cases of the Kepler problem and the N-body problem are used as specific examples. Series: Progress in Nonlinear Differential Equations and Their Applications. Num Pages: 172 pages, biography. BIC Classification: PBK. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 234 x 156 x 11. Weight in Grams: 426. . 1993. Hardback. . . . . Books ship from the US and Ireland. …

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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Thismonographdealswiththeexistenceofperiodicmotionsof Lagrangiansystemswith ndegreesoffreedom ij + V'(q) =0, where Visasingularpotential.Aprototypeofsuchaproblem, evenifitisnottheonlyphysicallyinterestingone,istheKepler problem . q 0 q+yqr= . This,jointlywiththemoregeneralN-bodyproblem,hasalways beentheobjectofagreatdealofresearch.Mostofthoseresults arebasedonperturbationmethods,andmakeuseofthespecific featuresoftheKeplerpotential. OurapproachismoreonthelinesofNonlinearFunctional Analysis:ourmainpurposeistogiveafunctionalframefor systemswithsingularpotentials,includingtheKeplerandthe N-bodyproblemasparticularcases.PreciselyweuseCritical PointTheorytoobtainexistenceresults,qualitativeinnature, whichholdtrueforbroadclassesofpotentials.Thishighlights thatthevariationalmethods,whichhavebeenemployedtoob tainimportantadvancesinthestudyofregularHamiltonian systems,canbesuccessfallyusedtohandlesingularpotentials aswell. Theresearchonthistopicisstillinevolution,andtherefore theresultswewillpresentarenottobeintendedasthefinal ones. Indeedamajorpurposeofourdiscussionistopresent methodsandtoolswhichhavebeenusedinstudyingsuchprob lems. Vlll PREFACE Partofthematerialofthisvolumehasbeenpresentedina seriesoflecturesgivenbytheauthorsatSISSA,Trieste,whom wewouldliketothankfortheirhospitalityandsupport. We wishalsotothankUgoBessi,PaoloCaldiroli,FabioGiannoni, LouisJeanjean,LorenzoPisani,EnricoSerra,KazunakaTanaka, EnzoVitillaroforhelpfulsuggestions. May26,1993 Notation n 1.For x, yE IR , x. ydenotestheEuclideanScalarproduct, and IxltheEuclideannorm. 2. meas(A)denotestheLebesguemeasureofthesubset Aof n IR 3.Wedenoteby ST =[0,T]/{a,T}theunitarycirclepara metrizedby t E[0,T].Wewillalsowrite SI= ST=I. n 1 n 4.Wewillwrite sn = {xE IR + : Ixl =I}andn = IR {O}. n 5.Wedenoteby LP([O,T], IR ),1~ p~+00,theLebesgue spaces,equippedwiththestandardnorm lIulip. l n l n 6. H (ST, IR )denotestheSobolevspaceof u E H ,2(0, T; IR ) suchthat u(O) = u(T).Thenormin HIwillbedenoted by lIull2 = lIull~ + lIull~ 7.Wedenoteby( 1 )and11 11respectivelythescalarproduct andthenormoftheHilbertspace E. 8.For uE E, EHilbertorBanachspace,wedenotetheball ofcenter uandradiusrby B(u,r) = {vE E: lIu- vii~ r}.Wewillalsowrite B = B(O, r). r 1 1 9.WesetA (n) = {uE H (St,n)}. k 10.For VE C (1Rxil,IR)wedenoteby V'(t, x)thegradient of Vwithrespectto x. l 11.Given f E C (M,IR), MHilbertmanifold,welet r = {uEM: f(u) ~ a}, f-l(a,b) = {uE E : a~ f(u) ~ b}. x NOTATION 12.Given f E C1(M,JR), MHilbertmanifold,wewilldenote by Zthesetofcriticalpointsof fon Mandby Zctheset Z U f-l(c, c). 13.Givenasequence UnE E, EHilbertspace,by Un ---'' Uwe willmeanthatthesequence Unconvergesweaklyto u. 14.With Pds. (E)wewilldenotethesetoflinearandcontinuous operatorson E. 15.With Ck''''(A,JR)wewilldenotethesetoffunctions ffrom AtoJR, ktimesdifferentiablewhosek-derivativeisHolder continuousofexponent0. Main Assumptions Wecollecthere,forthereader'sconvenience,themainassump tionsonthepotential Vusedthroughoutthebook. (VO) VEC1(lRXO,lR),V(t+T,x)=V(t,X) V(t,x)ElRXO, (VI) V(t,x) 176 pp. Englisch. …

Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. I Preliminaries.- II Singular Potentials.- III The Strongly Attractive Case.- IV The Weakly Attractive Case.- V Orbits with Prescribed Energy.- VI The N-Body Problem.- VII Perturbation Results.Thismonographdealswiththeexistenceofperiodicmotionsof Lagran.…

Buch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -I Preliminaries.- II Singular Potentials.- III The Strongly Attractive Case.- IV The Weakly Attractive Case.- V Orbits with Prescribed Energy.- VI The N-Body Problem.- VII Perturbation Results.Springer Nature c/o IBS, Benzstrasse 21, 48619 Heek 176 pp. Englisch.…