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008 150903s2013 xxu| o |||| 0|eng d
020 _a9781461485230
_99781461485230
024 7 _a10.1007/9781461485230
_2doi
035 _avtls000342508
039 9 _a201509030854
_bVLOAD
_c201405050244
_dVLOAD
_y201402061128
_zstaff
040 _aMX-SnUAN
_bspa
_cMX-SnUAN
_erda
050 4 _aQA372
100 1 _aPinasco, Juan Pablo.
_eautor
_9320906
245 1 0 _aLyapunov-type Inequalities :
_bWith Applications to Eigenvalue Problems /
_cby Juan Pablo Pinasco.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2013.
300 _axiii, 131 páginas
_brecurso en línea.
336 _atexto
_btxt
_2rdacontent
337 _acomputadora
_bc
_2rdamedia
338 _arecurso en línea
_bcr
_2rdacarrier
347 _aarchivo de texto
_bPDF
_2rda
490 0 _aSpringerBriefs in Mathematics,
_x2191-8198
500 _aSpringer eBooks
520 _aThe eigenvalue problems for quasilinear and nonlinear operators present many differences with the linear case, and a Lyapunov inequality for quasilinear resonant systems showed the existence of  eigenvalue asymptotics driven by the coupling of the equations instead of the order of the equations. For p=2, the coupling and the order of the equations are the same, so this cannot happen in linear problems.  Another striking difference between linear and quasilinear second order differential operators is the existence of Lyapunov-type inequalities in R^n when p>n. Since the linear case corresponds to p=2, for the usual Laplacian there exists a Lyapunov inequality only for one-dimensional problems. For linear higher order problems, several Lyapunov-type inequalities were found by Egorov and Kondratiev and collected in On spectral theory of elliptic operators, Birkhauser Basel 1996. However, there exists an interesting interplay between the dimension of the underlying space, the order of the differential operator, the Sobolev space where the operator is defined, and the norm of the weight appearing in the inequality which is not fully developed.   Also, the Lyapunov inequality for differential equations in Orlicz spaces can be used to develop an oscillation theory, bypassing the classical sturmian theory which is not known yet for those equations. For more general operators, like the p(x) laplacian, the possibility of existence of Lyapunov-type inequalities remains unexplored.  
590 _aPara consulta fuera de la UANL se requiere clave de acceso remoto.
710 2 _aSpringerLink (Servicio en línea)
_9299170
776 0 8 _iEdición impresa:
_z9781461485223
856 4 0 _uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/978-1-4614-8523-0
_zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
942 _c14
999 _c290267
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