×
Du, Juan; Cui, Minggen

Constructive proof of existence for a class of fourth-order nonlinear BVPs. (English) Zbl 1189.34038

Comput. Math. Appl. 59, No. 2, 903-911 (2010).
Summary: A new existence proof of solutions for a class of fourth-order nonlinear boundary value problems is proposed. The proof of the main results is based on the reproducing kernel theorem. It is worthwhile to point out that the method presented in this paper can be applied for the existence proof of diverse kinds of boundary conditions.

Cited in 11 Documents

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations

Keywords:

existence; nonlinear boundary value problems; reproducing kernel space; iterative sequence
PDF BibTeX XML Cite
\textit{J. Du} and \textit{M. Cui}, Comput. Math. Appl. 59, No. 2, 903--911 (2010; Zbl 1189.34038)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Bai, Z.; Wang, H., On positive solutions of some nonlinear fourth-order beam equations, J. math. anal. appl., 270, 357-368, (2002) · Zbl 1006.34023
[2] Li, F.; Zhang, Q.; Liang, Z., Existence and multiplicity of solutions of a kind of fourth-order boundary value problem, Nonlinear anal. TMA, 62, 803-816, (2005) · Zbl 1076.34015
[3] Liu, B., Positive solutions of fourth-order two point boundary value problems, Appl. math. comput., 148, 407-420, (2004) · Zbl 1039.34018
[4] Han, Guodong; Xu, Zongben, Multiple solutions of some nonlinear fourth-order beam equations, Nonlinear anal. TMA, 68, 3646-3656, (2008) · Zbl 1145.34008
[5] Carrião, P.C.; Faria, L.F.O.; Miyagaki, O.H., Periodic solutions for extended fisher – kolmogorov and Swift-Hohenberg equations by truncature techniques, Nonlinear analysis TMA, 67, 3076-3083, (2007) · Zbl 1128.34026
[6] Bai, Zhanbing, The upper and lower solution method for some fourth-order boundary value problems, Nonlinear analysis TMA, 67, 1704-1709, (2007) · Zbl 1122.34010
[7] Feng, H., Existence and uniqueness of solutions for a fourth-order boundary value problem, Nonlinear analysis TMA, (2008)
[8] Huanmin Yao, The research of algorithms for some singular differential equations of higher even-order, Ph.D. Thesis, Department of Mathematics, Harbin Institute of Technology, 2008
[9] Du, Juan; Cui, Minggen, Constructive approximation of solution for fourth-order nonlinear boundary value problems, Math. methods appl. sci., 32, 723-737, (2009) · Zbl 1170.34015
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.