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Keywords:
iterated differential equations; maximal and minimal solutions
iterated differential equations; maximal and minimal solutions
Summary:
In this paper we are concerned with sufficient conditions for the existence of minimal and maximal solutions of differential equations of the form
\[ L_{4}y+f(t,y)=0\,, \]
where $L_{4}y$ is the iterated linear differential operator of order $4$ and $f\colon [a,\infty )\times (0,\infty )\rightarrow (0,\infty )$ is a continuous function.
References:
[1] Barret, J. H.: Oscillation theory of ordinary linear differential equations. Adv. Math. 3 (1969), 415–509. DOI 10.1016/0001-8708(69)90008-5 | MR 0257462
[2] Fink, A. M., Kusano, T.: Nonoscillation theorems for differential equations with general deviating arguments. Lecture Notes in Math. 1032 (1983), 224–239. DOI 10.1007/BFb0076799 | MR 0742641 | Zbl 0531.34052
[3] Kusano, T., Swanson, C. A.: Asymptotic properties of semilinear elliptic equations. Funkcial. Ekvac. 26 (1983), 115–129. MR 0736896 | Zbl 0536.35024
[4] Kusano, T., Swanson, C. A.: Asymptotic theory of singular semilinear elliptic equations. Canad. Math. Bull. 27 (1984), 223–232. DOI 10.4153/CMB-1984-032-1 | MR 0740418 | Zbl 0589.35046
[5] Neuman, F.: Oscillatory behavior of iterative linear ordinary differential equations depends on their order. Arch. Math. (Brno) 22 (4) (1986), 187–192. MR 0868533 | Zbl 0608.34036
[6] Pólya, G.: On the mean-value theorem corresponding to a given linear homogeneous differential equations. Trans. Amer. Math. Soc. 24 (1922), 312–324. DOI 10.2307/1988819 | MR 1501228
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