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001			978-1-4614-8523-0
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008			130914s2013 xxu| s |||| 0|eng d
020			_a9781461485230 _9978-1-4614-8523-0
024	7		_a10.1007/978-1-4614-8523-0 _2doi
050		4	_aQA372
072		7	_aPBKJ _2bicssc
072		7	_aMAT007000 _2bisacsh
082	0	4	_a515.352 _223
100	1		_aPinasco, Juan Pablo. _eauthor.
245	1	0	_aLyapunov-type Inequalities _h[electronic resource] : _bWith Applications to Eigenvalue Problems / _cby Juan Pablo Pinasco.
264		1	_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c2013.
300			_aXIII, 131 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aSpringerBriefs in Mathematics, _x2191-8198
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.
650		0	_aMathematics.
650		0	_aFunctional equations.
650		0	_aDifferential Equations.
650		0	_aDifferential equations, partial.
650	1	4	_aMathematics.
650	2	4	_aOrdinary Differential Equations.
650	2	4	_aSeveral Complex Variables and Analytic Spaces.
650	2	4	_aDifference and Functional Equations.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781461485223
830		0	_aSpringerBriefs in Mathematics, _x2191-8198
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4614-8523-0
912			_aZDB-2-SMA
999			_c96064 _d96064