×
Yang, Zhilin; O’Regan, Donal

Positive solvability of systems of nonlinear Hammerstein integral equations. (English) Zbl 1079.45005

J. Math. Anal. Appl. 311, No. 2, 600-614 (2005).
Authors’ summary: The paper deals with the existence of positive continuous solutions to systems of nonlinear Hammerstein integral equations. The main tool used in the proofs is fixed point index theory in a cone. The results obtained here are essentially different from existing ones in the literature.

Cited in 25 Documents

MSC:

45G15 Systems of nonlinear integral equations
45M20 Positive solutions of integral equations

Keywords:

system of integral equations; positive solution; cone; boundary problem; concave function; nonlinear Hammerstein integral equation; fixed point index theory
PDF BibTeX XML Cite
\textit{Z. Yang} and \textit{D. O'Regan}, J. Math. Anal. Appl. 311, No. 2, 600--614 (2005; Zbl 1079.45005)
Full Text: DOI

References:

[1] Hammerstein, A., Nichtlineare Integralgleichungen nebst Anwendungen, Acta Math., 54, 117-176 (1929) · JFM 56.0343.03
[2] Guo, D.; Sun, J., Nonlinear Integral Equations (1987), Shandong Press of Science and Technology: Shandong Press of Science and Technology Jinan, (in Chinese)
[3] Krasnoselskii, M. A., Topological Methods in the Theory of Nonlinear Integral Equations (1964), Pergamon: Pergamon Oxford
[4] Sun, J.; Liu, X., Computation for topological degree and its applications, J. Math. Anal. Appl., 202, 785-796 (1996) · Zbl 0866.47043
[5] Zhang, Z., Existence of non-trivial solutions for superlinear systems of integral equations and applications, Acta Math. Sinica, 15, 153-162 (1999) · Zbl 0941.45002
[6] Wang, J., Existence of nontrivial solutions to nonlinear systems of Hammerstein integral equations and applications, Indian J. Pure Appl. Math., 31, 1303-1311 (2001) · Zbl 0976.45004
[7] Guo, D.; Lakshmikantham, V., Nonlinear Problems in Abstract Cones (1988), Academic Press: Academic Press Boston · Zbl 0661.47045
[8] Deimling, K., Nonlinear Functional Analysis (1985), Springer-Verlag · Zbl 0559.47040
[9] Krein, M. G.; Rutman, M. A., Linear operators leaving invariant a cone in a Banach space, Transl. Amer. Math. Soc., 10, 199-325 (1962) · Zbl 0030.12902
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.