Comparison and oscillation theorems for matrix differential inequalitites

Noussair, E. S.

doi:10.1090/S0002-9947-1971-0280846-X

Comparison and oscillation theorems for matrix differential inequalitites
HTML articles powered by AMS MathViewer

by E. S. Noussair

Trans. Amer. Math. Soc. 160 (1971), 203-215

DOI: https://doi.org/10.1090/S0002-9947-1971-0280846-X

PDF | Request permission

Abstract:

Strong comparison theorems of Sturm’s type are established for systems of second order quasilinear elliptic partial differential equations. The technique used leads to new oscillation and nonoscillation criteria for such systems. Some criteria are deduced from a comparison theorem, and others are derived by a direct variational method. Some of our results constitute extensions of known theorems to nonselfadjoint quasilinear systems.

References

Shmuel Agmon, Lectures on elliptic boundary value problems, Van Nostrand Mathematical Studies, No. 2, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1965. Prepared for publication by B. Frank Jones, Jr. with the assistance of George W. Batten, Jr. MR 0178246

Sturm separation and comparison theorems for ordinary and partial differential equations

F. R. Gantmaher, Teoriya matric, Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow, 1953 (Russian). MR 0065520
Einar Hille, Non-oscillation theorems, Trans. Amer. Math. Soc. 64 (1948), 234–252. MR 27925, DOI 10.1090/S0002-9947-1948-0027925-7
Kurt Kreith, A strong comparison theorem for selfadjoint elliptic equations, Proc. Amer. Math. Soc. 19 (1968), 989–990. MR 227594, DOI 10.1090/S0002-9939-1968-0227594-5
L. M. Kuks, Sturm’s theorem and the oscillation of solutions of strongly elliptic systems, Dokl. Akad. Nauk SSSR 142 (1962), 32–35 (Russian). MR 0142874
Marston Morse, A generalization of the sturm separation and comparison theorems in $n$-space, Math. Ann. 103 (1930), no. 1, 52–69. MR 1512617, DOI 10.1007/BF01455690
C. A. Swanson, Comparison theorems for elliptic differential systems, Pacific J. Math. 33 (1970), 445–450. MR 262650, DOI 10.2140/pjm.1970.33.445
C. A. Swanson, Oscillatory criteria for nonlinear matrix differential inequalities, Proc. Amer. Math. Soc. 24 (1970), 824–827. MR 259248, DOI 10.1090/S0002-9939-1970-0259248-2