000 | 03236nam a22004937a 4500 | ||
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001 | sulb-eb0022936 | ||
003 | BD-SySUS | ||
005 | 20160413122326.0 | ||
007 | cr nn 008mamaa | ||
008 | 130914s2013 xxu| s |||| 0|eng d | ||
020 |
_a9781461485230 _9978-1-4614-8523-0 |
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024 | 7 |
_a10.1007/978-1-4614-8523-0 _2doi |
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050 | 4 | _aQA372 | |
072 | 7 |
_aPBKJ _2bicssc |
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072 | 7 |
_aMAT007000 _2bisacsh |
|
082 | 0 | 4 |
_a515.352 _223 |
100 | 1 |
_aPinasco, Juan Pablo. _eauthor. |
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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. |
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300 |
_aXIII, 131 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aSpringerBriefs in Mathematics, _x2191-8198 |
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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 | _aDifference equations. | |
650 | 0 | _aFunctional equations. | |
650 | 0 | _aDifferential equations. | |
650 | 0 | _aFunctions of complex variables. | |
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 | ||
942 |
_2Dewey Decimal Classification _ceBooks |
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999 |
_c45028 _d45028 |