Previous |  Up |  Next

Article

Keywords:
oscillatory; second order differential equations
Summary:
We give a sufficient condition for the oscillation of linear homogeneous second order differential equation $y^{\prime \prime }+p(x)y^{\prime }+q(x)y=0$, where $p(x), q(x)\in C[\alpha ,\infty )$ and $\alpha $ is positive real number.
References:
[1] A. Sauer: A note of zero-sequences of solutions of $f^{\prime \prime }+Af=0$. Amer. Math. Soc. 125 (1997), 1143–1147. DOI 10.1090/S0002-9939-97-03819-7 | MR 1377005
[2] G. J. Butler, I. H. Erbe and A. B. Mingarelli: Riccati techniques and variational principles in oscillation theory for linear systems. Trans. Amer. Math. Soc. 303 (1987), 263–282. DOI 10.1090/S0002-9947-1987-0896022-5 | MR 0896022
[3] H.  Erbe, Qinghai Kong and Shigui Ruan: Kamenev type theorems for 2nd order matrix differential systems. Proc. Amer. Math. Soc. 117 (1993), 957–962. MR 1154244
[4] E.  Hille: Non-oscillation theorems. Trans. Amer. Math. Soc. 64 (1948), 234–252. DOI 10.1090/S0002-9947-1948-0027925-7 | MR 0027925 | Zbl 0031.35402
[5] I.  Kamenev: Integral criterion for oscillation of linear differential equations of second order. Zametki 23 (1978), 136-138. MR 0486798 | Zbl 0408.34031
[6] J. W. Macki and J. S. W.  Wong: Oscillation theorems for linear second order differential equations. Proc. Amer. Math. Soc. 20 (1969), 67–72. DOI 10.1090/S0002-9939-1969-0235202-3 | MR 0235202
[7] A. B. Mingarelli: On a conjecture for oscillation of second order ordinary differential systems. Proc. Amer. Math. Soc. 82 (1981), 592–598. MR 0614884 | Zbl 0487.34030
[8] Ch. G.  Philos and I. K. Purnaras: Oscillations in superliner differential equations of second order. J. Math. Anal. Appl. 165 (1992), 1–11. DOI 10.1016/0022-247X(92)90065-L | MR 1151058
[9] D.  Willett: On the oscillatory behavior of the solution of second order linear differential equations. Ann. Polon. Math. 21 (1969), 175–194. DOI 10.4064/ap-21-2-175-194 | MR 0249723
[10] J.  Yan: A note on an oscillation criterion for an equation with damped term. Proc. Amer. Math. Soc. 90 (1984), 277–280. DOI 10.1090/S0002-9939-1984-0727249-3 | MR 0727249 | Zbl 0542.34028
Partner of
EuDML logo