Rankin: Strong oscillation of elliptic systems of second order partial differential equations

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 Serie 8 59 (1975), fasc. n.6, p. 595-602, (English)
pdf (610 Kb), djvu (850 Kb). | MR 0492761 | Zbl 0352.35012

Sunto

Si dà una condizione sufficiente ad assicurare il carattere fortemente oscillatorio dei sistemi ellittici del tipo $$\sum_{i,j=1}^{n} \, D_{i}(A_{ij}(x) \, D_{j}u) + C(x) \, u = 0.$$ Con questo risultato si estendono vari criteri noti relativi al caso di una sola equazione.

Referenze Bibliografiche

[1] C. CLARK and C. A. SWANSON (1965) - Comparison theorems for elliptic differential equations, «Proceedings of American Mathematical Society», 16, 886-890. | fulltext (doi) | MR 180753 | Zbl 0134.09001

[2] R. COURANT and D. HILBERT (1937) - Methods of Mathematical Physic, Interscience Publishers, New York. | MR 65391

[3] V. B. HEADLEY (1970) - Some oscillation properties of self-adjoint elliptic equations, «Proc. Amer. Math. Society», 21, 824-829. | fulltext (doi) | MR 259323 | Zbl 0197.37201

[4] V. B. HEADLY and C. A. SWANSON (1968) - Oscillation criteria for elliptic equations, «Pacific Journal of Mathematics », 27 (3), 501-506. | MR 236502 | Zbl 0165.44304

[5] KURT KREITH (1963) - A new proof of a comparison theorem for elliptic equations, «Proc. Amer. Math. Soc.», 14, 33-35. | fulltext (doi) | MR 149067

[6] KURT KREITH (1968) - A strong comparison theorem for self-adjoint elliptic equations, «Proc. Amer. Math. Soc.», 19, 989-990. | fulltext (doi) | MR 227594 | Zbl 0159.39802

[7] KURT KREITH (1969) - A Sturm theorem for strongly elliptic systems and applications, «Bulletin of the Amer. Math. Soc.», 75, 1025-1027. | fulltext (doi) | MR 249824 | Zbl 0179.43104

[8] K. KREITH and C. C. TRAVIS (1971) - On a comparison theorem for strongly elliptic systems, «Journal of Differential Equations», 10, 173-178. | fulltext (doi) | MR 294842 | Zbl 0214.35904

[9] K. KREITH and C. TRAVIS (1972) - Oscillation criteria for self-adjoint elliptic equations, «Pacific Journal of Mathematics», 41, 743-753. | MR 318642 | Zbl 0239.35003

[10] S. RANKIN (1974) - Oscillation theory for second order elliptic partial differential equations, Ph. D. thesis, Vanderbilt University, December, 1974. | MR 2624996

[11] C. A. SWANSON (1970) - Comparison theorems for elliptic differential systems, «Pacific Journal of Math.», 33, 445-450. | MR 262650 | Zbl 0177.14703

[12] C. A. SWANSON (1973) - Strong oscillation of elliptic equations in general domains, «Canadian Mathematical Bulletin», 16, 105-110. | fulltext (doi) | MR 333415 | Zbl 0253.35026

[13J C. TRAVIS (1973) - A remark on integral oscillation criteria for self-adjoint elleptic equations, «Accademia Nazionale dei Lincei», 54, 829-831. | MR 361397

[14] C. TRAVIS - Oscillation criteria of elliptic systems (to appear).

bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Sunto

Referenze Bibliografiche