Si dà una condizione sufficiente ad assicurare il carattere fortemente oscillatorio dei sistemi ellittici del tipo Con questo risultato si estendono vari criteri noti relativi al caso di una sola equazione.
@article{RLINA_1975_8_59_6_595_0, author = {Samuel M. Rankin}, title = {Strong oscillation of elliptic systems of second order partial differential equations}, journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti}, volume = {59}, year = {1975}, pages = {595-602}, zbl = {0352.35012}, mrnumber = {0492761}, language = {en}, url = {http://dml.mathdoc.fr/item/RLINA_1975_8_59_6_595_0} }
Rankin, Samuel M. Strong oscillation of elliptic systems of second order partial differential equations. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 59 (1975) pp. 595-602. http://gdmltest.u-ga.fr/item/RLINA_1975_8_59_6_595_0/
[1] Comparison theorems for elliptic differential equations, «Proceedings of American Mathematical Society», 16, 886-890. | MR 180753 | Zbl 0134.09001
and (1965) -[2] | MR 65391
and (1937) - Methods of Mathematical Physic, Interscience Publishers, New York.[3] Some oscillation properties of self-adjoint elliptic equations, «Proc. Amer. Math. Society», 21, 824-829. | MR 259323 | Zbl 0197.37201
(1970) -[4] Oscillation criteria for elliptic equations, «Pacific Journal of Mathematics », 27 (3), 501-506. | MR 236502 | Zbl 0165.44304
and (1968) -[5] A new proof of a comparison theorem for elliptic equations, «Proc. Amer. Math. Soc.», 14, 33-35. | MR 149067
(1963) -[6] A strong comparison theorem for self-adjoint elliptic equations, «Proc. Amer. Math. Soc.», 19, 989-990. | MR 227594 | Zbl 0159.39802
(1968) -[7] A Sturm theorem for strongly elliptic systems and applications, «Bulletin of the Amer. Math. Soc.», 75, 1025-1027. | MR 249824 | Zbl 0179.43104
(1969) -[8] On a comparison theorem for strongly elliptic systems, «Journal of Differential Equations», 10, 173-178. | MR 294842 | Zbl 0214.35904
and (1971) -[9] Oscillation criteria for self-adjoint elliptic equations, «Pacific Journal of Mathematics», 41, 743-753. | MR 318642 | Zbl 0239.35003
and (1972) -[10] Oscillation theory for second order elliptic partial differential equations, Ph. D. thesis, Vanderbilt University, December, 1974. | MR 2624996
(1974) -[11] Comparison theorems for elliptic differential systems, «Pacific Journal of Math.», 33, 445-450. | MR 262650 | Zbl 0177.14703
(1970) -[12] Strong oscillation of elliptic equations in general domains, «Canadian Mathematical Bulletin», 16, 105-110. | MR 333415 | Zbl 0253.35026
(1973) -[13J A remark on integral oscillation criteria for self-adjoint elleptic equations, «Accademia Nazionale dei Lincei», 54, 829-831. | MR 361397
(1973) -[14] Oscillation criteria of elliptic systems (to appear).
-