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Positive solutions of fourth-order superlinear singular boundary value problems

Published online by Cambridge University Press:  17 April 2009

Guoliang Shi
Affiliation:
Department of Mathematics, Shandong University, Jinan, Shandong 250100, People's Republic of China e-mail: szchen@sdu.eud.cn
Shaozhu Chen
Affiliation:
Department of Mathematics, Shandong University, Jinan, Shandong 250100, People's Republic of China e-mail: szchen@sdu.eud.cn
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Abstract

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This paper investigates fourth-order superlinear singular two-point boundary value problems and obtains necessary and sufficient conditions for existence of C2 or C3 positive solutions on the closed interval.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Aftabizadeh, A.R., ‘Existence and uniqueness theorems for fourth-order boundary value problems’, J. Math. Anal. Appl. 116 (1986), 415426.CrossRefGoogle Scholar
[2]Agarwal, R.P., ‘On fourth-order boundary value problems arising in beam analysis’, Differential Integral Equations 2 (1989), 91110.CrossRefGoogle Scholar
[3]Graef, J.R. and Yang, B., ‘Existence and nonexistence of positive solutions of fourth order nonlinear boundary value problem’, Appl. Anal. 74 (2000), 201214.CrossRefGoogle Scholar
[4]Graef, J.R. and Yang, B., ‘On a nonlinear boundary value problems for fourth order equations’, Appl. Anal. 72 (1999), 439451.CrossRefGoogle Scholar
[5]Ma, R. and Wang, H., ‘On the existence of positive solutions of fourth-order ordinary differential equations’, Appl. Anal. 59 (1995), 225231.Google Scholar
[6]Ma, R., Zhang, J., and Fu, S., ‘The method of lower and upper solutions for fourth-order two-point boundary value problems’, J. Math. Anal. Appl. 215 (1997), 415422.Google Scholar
[7]Yang, Y., ‘Fourth-order two-point boundary value problems’, Proc. Amer. Math. Soc. 104 (1988), 175180.CrossRefGoogle Scholar
[8]O'Regan, D., ‘Solvability of some fourth (and higher) order singular boundary value problems’, J. Math. Anal. Appl. 161 (1991), 78116.CrossRefGoogle Scholar
[9]Wei, Z., ‘Positive solutions of singular boundary value problems of fourth order differential equations’, Acta Math. Sinica 42 (1999), 715722.Google Scholar
[10]Chen, S. and Zhang, Y., ‘Singular boundary value problem on a half-line’, J. Math. Anal. Appl. 195 (1995), 449468.CrossRefGoogle Scholar
[11]Guo, D. and Lakshmikantham, V., Nonlinear problems in abstract cones, Notes and Reports in Mathematics in Science and Engineering 5 (Academic Press, Inc., Boston, New York, 1988).Google Scholar