Geodesic
Strong oscillation of elliptic systems of second order partial differential equations
Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 59 (1975) no. 6, pp. 595-602 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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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. 
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     title = {Strong oscillation of elliptic systems of second order partial differential equations},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali},
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Rankin, Samuel M. Strong oscillation of elliptic systems of second order partial differential equations. Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 59 (1975) no. 6, pp. 595-602. http://geodesic.mathdoc.fr/item/RLINA_1975_8_59_6_a0/

[1] C. Clark and C. A. Swanson (1965) - Comparison theorems for elliptic differential equations, «Proceedings of American Mathematical Society», 16, 886-890. | DOI | MR | Zbl

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

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

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

[5] Kurt Kreith (1963) - A new proof of a comparison theorem for elliptic equations, «Proc. Amer. Math. Soc.», 14, 33-35. | DOI | MR

[6] Kurt Kreith (1968) - A strong comparison theorem for self-adjoint elliptic equations, «Proc. Amer. Math. Soc.», 19, 989-990. | DOI | MR | Zbl

[7] Kurt Kreith (1969) - A Sturm theorem for strongly elliptic systems and applications, «Bulletin of the Amer. Math. Soc.», 75, 1025-1027. | DOI | MR | Zbl

[8] K. Kreith and C. C. Travis (1971) - On a comparison theorem for strongly elliptic systems, «Journal of Differential Equations», 10, 173-178. | DOI | MR | Zbl

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

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

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

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

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

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