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Positive solutions of fourth-order two point boundary value problems. (English) Zbl 1039.34018

Summary: By using the Krasnoselskii fixed-point theorem, we study the existence of one or multiple positive solution of the fourth-order two-point boundary value problem \(y^{(4)}(t)=f(t,y(t),y''(t))\), \(y(0)=y(1)=y''(0)=y''(1)=0\). We also give some examples to illustrate our results.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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[1] Aftabizadeh, A. R., Existence and uniqueness theorems for fourth-order boundary problems, J. Math. Anal. Appl., 116, 415-426 (1986) · Zbl 0634.34009
[2] Yang, Yisong, Fourth-order two-point boundary value problem, Proc. Am. Math. Soc., 104, 175-180 (1988) · Zbl 0671.34016
[3] Del Pino, M. A.; Manasevich, R. F., Existence for fourth-order boundary value problem under a two-parameter nonresonance condition, Proc. Am. Math. Soc., 112, 81-86 (1991) · Zbl 0725.34020
[4] Gupta, C. P., Existence and uniqueness theorem for a bending of an elastic beam equation, Appl. Anal., 26, 289-304 (1988) · Zbl 0611.34015
[5] Gupta, C. P., Existence and uniqueness results for some fourth order fully quasilinear boundary value problem, Appl. Anal., 36, 169-175 (1990)
[6] Ma, Ruyun; Wang, Haiyai, On the existence of positive solutions of fourth order ordinary differential equations, Appl. Anal., 59, 225-231 (1995) · Zbl 0841.34019
[7] Ma, Ruyan, Positive solutions of fourth-order two point boundary value problems, Ann. Differen. Equations, 15, 305-313 (1999) · Zbl 0964.34021
[8] Deimling, K., Nonlinear Functional Analysis (1985), Springer: Springer New York · Zbl 0559.47040
[9] Krasnoselskii, M. A., Postive solution of Operator Equations (1964), Noordhoff: Noordhoff Gronignen
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