Lyapunov-type inequalities: with applications to eigenvalue problems
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Springer
2013
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| Schriftenreihe: | SpringerBriefs in mathematics
|
| Schlagworte: | |
| Online-Zugang: | BTU01 TUM01 UBA01 UBM01 UBT01 UBW01 UPA01 Volltext Abstract |
| Beschreibung: | 1 Online-Ressource |
| ISBN: | 9781461485223 9781461485230 |
| DOI: | 10.1007/978-1-4614-8523-0 |
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Datensatz im Suchindex
| _version_ | 1804151478415261696 |
|---|---|
| adam_text | LYAPUNOV-TYPE INEQUALITIES
/ PINASCO, JUAN PABLO
: 2013
ABSTRACT / INHALTSTEXT
THE 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.
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Pinasco, Juan Pablo |
| author_facet | Pinasco, Juan Pablo |
| author_role | aut |
| author_sort | Pinasco, Juan Pablo |
| author_variant | j p p jp jpp |
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| dewey-full | 610 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 610 - Medicine and health |
| dewey-raw | 610 |
| dewey-search | 610 |
| dewey-sort | 3610 |
| dewey-tens | 610 - Medicine and health |
| discipline | Mathematik Medizin |
| doi_str_mv | 10.1007/978-1-4614-8523-0 |
| format | Electronic eBook |
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| spelling | Pinasco, Juan Pablo Verfasser aut Lyapunov-type inequalities with applications to eigenvalue problems Juan Pablo Pinasco New York, NY [u.a.] Springer 2013 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier SpringerBriefs in mathematics Eigenwertproblem (DE-588)4013802-1 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Eigenwertproblem (DE-588)4013802-1 s Gewöhnliche Differentialgleichung (DE-588)4020929-5 s 1\p DE-604 https://doi.org/10.1007/978-1-4614-8523-0 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026830037&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Abstract 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Pinasco, Juan Pablo Lyapunov-type inequalities with applications to eigenvalue problems Eigenwertproblem (DE-588)4013802-1 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4013802-1 (DE-588)4020929-5 |
| title | Lyapunov-type inequalities with applications to eigenvalue problems |
| title_auth | Lyapunov-type inequalities with applications to eigenvalue problems |
| title_exact_search | Lyapunov-type inequalities with applications to eigenvalue problems |
| title_full | Lyapunov-type inequalities with applications to eigenvalue problems Juan Pablo Pinasco |
| title_fullStr | Lyapunov-type inequalities with applications to eigenvalue problems Juan Pablo Pinasco |
| title_full_unstemmed | Lyapunov-type inequalities with applications to eigenvalue problems Juan Pablo Pinasco |
| title_short | Lyapunov-type inequalities |
| title_sort | lyapunov type inequalities with applications to eigenvalue problems |
| title_sub | with applications to eigenvalue problems |
| topic | Eigenwertproblem (DE-588)4013802-1 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Eigenwertproblem Gewöhnliche Differentialgleichung |
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