## Abstract Oscillation criteria for selfβadjoint fourthβorder differential equations were established for various conditions on the coefficients __r__(__x__) > 0, __q__(__x__) and __p__(__x__). However, most of these results deal with the case when lim~__x__ β β~β«^__x__^~1~__q__(__s__)β__ds__ < +
Oscillation and Discreteness Criteria of Certain Fourth Order Elliptic Differential Operators
β Scribed by Frank Fiedler
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 408 KB
- Volume
- 187
- Category
- Article
- ISSN
- 0025-584X
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π SIMILAR VOLUMES
## Abstract This paper extends the results of the two previous papers in several directions. For one we allow slower decay of the coefficients, but higher order differentiability. For this an expansion for the diagonalizing transformations is derived. Secondly unbounded coefficients are permitted.
## Abstract We study the spectral theory of differential operators of the form on β^2^~__w__~ (0, β). By means of asymptotic integration, estimates for the eigenfunctions and__M__ βmatrix are derived. Since the __M__ βfunction is the Stieltjes transform of the spectral measure, spectral properties
HILBERT space L,(D) where the coefficients always fulfil the following conditions. ## i) ii) a@), q(z) E Cl(l2) and real-valued, a&) = a@), x E D, ( 7) Denoting the domain of the FRIEDRICHS extension A by D(A) we have W ) r H A . 5 mR"). 1) W#W) is the completion of Com(Rn) in the norm Ilullw&BT8