A Picone integral identity for a class of fourth order elliptic differential inequalities

D. R. Dunninger

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1971)

  • Volume: 50, Issue: 6, page 630-641
  • ISSN: 0392-7881

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Dunninger, D. R.. "A Picone integral identity for a class of fourth order elliptic differential inequalities." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 50.6 (1971): 630-641. <http://eudml.org/doc/296256>.

@article{Dunninger1971,
author = {Dunninger, D. R.},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
language = {eng},
month = {6},
number = {6},
pages = {630-641},
publisher = {Accademia Nazionale dei Lincei},
title = {A Picone integral identity for a class of fourth order elliptic differential inequalities},
url = {http://eudml.org/doc/296256},
volume = {50},
year = {1971},
}

TY - JOUR
AU - Dunninger, D. R.
TI - A Picone integral identity for a class of fourth order elliptic differential inequalities
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1971/6//
PB - Accademia Nazionale dei Lincei
VL - 50
IS - 6
SP - 630
EP - 641
LA - eng
UR - http://eudml.org/doc/296256
ER -

References

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  1. INCE, E. L., Ordinary Differential Equations, Dover, New York, 1956. 
  2. PICONE, M., Un teorema sulle soluzioni delle equazioni lineari ellittiche autoaggiunte alle derivate parziali del secondo-ordine, «Atti Accad. Naz. Lincei Rend.», 20, 213-219 (1911). Zbl42.0391.01
  3. KREITH, K., A generalized Picone identity, «Atti Accad. Naz. Lincei Rend.», 45, 217-220 (1968). Zbl0194.42002
  4. KREITH, K., A comparison theorem for general elliptic equations with mixed boundary conditions, «J. Diff. Eq.», 8, 537-541 (1970). Zbl0206.11304
  5. DUNNINGER, D. R., A Picone identity for non-self-adjoint elliptic operators, «Atti Accad. Naz. Lincei Rend.», 48, 133-139 (1970). Zbl0195.39403
  6. DUNNINGER, D. R. and WEINACHT, R. J., Separation and comparison theorems for classes of singular elliptic inequalities and degenerate elliptic inequalities (to appear). Zbl0213.37703
  7. KREITH, K., A comparison theorem for fourth order differential equations, «Atti Accad. Naz. Lincei Rend.», 46, 664-666 (1969). Zbl0188.14603
  8. SWANSON, C. A., A generalization of Sturm's comparison theorem, «J. Math. Anal. Appl.», 15, 512-519 (1966). Zbl0144.36301MR204820DOI10.1016/0022-247X(66)90105-3
  9. DIAZ, J. B. and DUNNINGER, D. R., Sturm separation and comparison theorems for a class of fourth order ordinary and partial differential equations (to appear). Zbl0319.35009MR397122DOI10.1080/00036817508839101
  10. DIAZ, J. B. and DUNNINGER, D. R., Sturmian theorems for a class of elliptic equations of order 2 m (to appear). Zbl0304.35004MR470427DOI10.1080/00036817408839075
  11. CIMMINO, G., Sulle equazioni lineari ellittiche autoaggiunte alle derivate parziali di ordine superiore al secondo, «Atti Accad. Naz. Lincei Mem.», 1, 59-69 (1930). Zbl56.0427.01
  12. AGMON, S., Lectures on Elliptic Boundary Value Problems, Van Nostrand, Princeton, 1965. Zbl0142.37401MR178246
  13. ALLEGRETTO, W., A comparison theorem for nonlinear elliptic operators (to appear). Zbl0225.35013MR298181
  14. SWANSON, C. A., Comparison theorems for elliptic differential systems, «Pacific J. Math.», 33, 445-450 (1970). Zbl0177.14703MR262650
  15. BEESACK, P. R., Integral inequalities of the Wirtinger type, «Duke Math. J.», 25, 477-498 (1958). Zbl0082.27104MR97478
  16. WONG, P. K., Integral inequalities of Wirtinger-type and fourth order elliptic differential inequalities (to appear). Zbl0228.35037MR306686
  17. BARTA, J., Sur la vibration fondamentale d'une membrane, «C. R. Acad. Sci.», 204, 472-473 (1937). Zbl63.0762.02
  18. PROTTER, M. H. and WEINBERGER, H. F., On the spectrum of general second order operators, «Bull. Amer. Math. Soc.», 72, 251-255 (1966). Zbl0141.09901MR190527DOI10.1090/S0002-9904-1966-11485-4

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