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Kang, Ping; Wei, Zhongli; Xu, Juanjuan

Positive solutions to fourth-order singular boundary value problems with integral boundary conditions in abstract spaces. (English) Zbl 1169.34043

Appl. Math. Comput. 206, No. 1, 245-256 (2008).
The authors discuss the existence of positive solutions for some 4th-order singular boundary value problems with integral boundary conditions in Banach spaces. Some interesting results are obtained by using the fixed point theory in cone. The results improve many previous works in the same field. Some example is provided for illustration.
Reviewer: Khalil Ezzinbi (Marrakech)

Cited in 19 Documents

MSC:

34G20 Nonlinear differential equations in abstract spaces
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations

Keywords:

positive solutions; fixed points; boundary value problems; integral boundary conditions
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\textit{P. Kang} et al., Appl. Math. Comput. 206, No. 1, 245--256 (2008; Zbl 1169.34043)
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References:

[1] Agarwal, R., On fourth-order boundary value problems arising in beam analysis, Diff. Inte. Eq., 2, 91-110 (1989) · Zbl 0715.34032
[2] Ma, H., Positive solutions for \(m\)-point boundary value problems of fourth order, J. Math. Anal. Appl., 321, 37-49 (2006) · Zbl 1101.34014
[3] Guo, D.; Lakshmikantham, V., Multiple solutions of two-point boundary value problems of ordinary differential equations in Banach spaces, J. Math. Anal. Appl., 129, 211-222 (1998) · Zbl 0645.34014
[4] Ma, R., On the existence of positive solutions of fourth order ordinary differential equations, Appl. Anal., 59, 225-231 (1995) · Zbl 0841.34019
[5] Wei, Z.; Zhang, Z., A necessary and sufficient condition for the existence of positive solutions to a class of singular superlinear boundary value problems, Acta Math. Sinica, 48, 25-34 (2005), (in Chinese) · Zbl 1124.34316
[6] O’Regan, D., Solvability of some fourth(and higher) order singular boundary value problems, J. Math. Anal. Appl., 161, 78-116 (1998) · Zbl 0795.34018
[7] Pang, C.; Wei, Z., The existence of two positive solutions of singular boundary value problems of fourth order differential equations, Acta Math. Sinica, 46, 403-410 (2003), (in Chinese) · Zbl 1136.34304
[8] Rynne, B., Infinitely many solutions of superlinear fourth order boundary value problems, Topol. Methods Nonlinear Anal., 19, 303-312 (2002) · Zbl 1017.34015
[9] Zhou, Y., Positive solutions of fourth order nonlinear eigenvalue problems, J. Sys. Sci. Math. Scis., 24, 433-442 (2004), (in Chinese) · Zbl 1069.34038
[10] Ma, R.; Zhang, J.; Fu, S., The method of lower and upper solutions for fourth-order two-point boundary value problems, J. Math. Anal. Appl., 215, 415-422 (1997) · Zbl 0892.34009
[12] Liu, Y., Multiple positive solutions to fourth-order singular boundary value problems in abstract spaces, Electron. J. Diff. Eqns., 120, 1-13 (2004)
[13] Guo, D.; Lakshmikantham, V.; Liu, X., Nonlinear Integral Equations in Abstract Spaces (1996), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0866.45004
[14] Lakshmikantham, V.; Leela, S., Nonlinear Differential Equations in Abstract Spaces (1981), Pergamon: Pergamon Oxford · Zbl 0456.34002
[15] Deimling, K., Ordinary Differential Equations in Banach Spaces (1977), Springer-Verlag · Zbl 0364.34030
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