On the existence of positive solutions of fourth-order ordinary differential equations. (English) Zbl 0841.34019

We study the existence of positive solutions of the equations \[ {d^4 y\over dx^4}- h(x) f(y(x))= 0 \] with either \(y(0)= y(1)= y''(0)= y''(1)= 0\) or \(y(0)= y'(1)= y''(0)= y'''(1)= 0\). We show the existence of at least one positive solution if \(f\) is either superlinear or sublinear by a simple application of a fixed point theorem in cones.
Reviewer: Ma Ruyun (Lanzhou)


34B15 Nonlinear boundary value problems for ordinary differential equations
34C11 Growth and boundedness of solutions to ordinary differential equations
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[1] Usmnir R. A., Proc. Amcr. Math. Soc. 77 pp 327– (1979)
[2] Yisong Yang, Proc. Amcr. Math. Soc. t 104 pp 175– (1988) · doi:10.1090/S0002-9939-1988-0958062-3
[3] Gupta C. P., Ap-pl. Analysist 26 pp 289– (1988) · Zbl 0611.34015 · doi:10.1080/00036818808839715
[4] Gupta C. P., J. Math. Anal. Appl. 135 pp 208– (1988) · Zbl 0655.73001 · doi:10.1016/0022-247X(88)90149-7
[5] Gupta C. P., Appl. Adysis 36 pp 157– (1990)
[6] Dajun Guo, Science and Tech (1985)
[7] Krasnoselskii R.A., Positive Solutions of Operator Equations (1964)
[8] Haiyan Wang, J. Differential Equotiar 109 pp 1– (1994) · Zbl 0798.34030 · doi:10.1006/jdeq.1994.1042
[9] RuyunSome Ma, Applied Mathemaics and Mechanics 14 pp 193– (1993) · Zbl 0776.73037 · doi:10.1007/BF02453362
[10] Fink A. M., J. Math. Anal. Appl. 180 pp 93– (1993) · Zbl 0807.34024 · doi:10.1006/jmaa.1993.1385
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