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

##### MSC:
 45G15 Systems of nonlinear integral equations 45M20 Positive solutions of integral equations
Full Text:
##### References:
 [1] Hammerstein, A.: Nichtlineare integralgleichungen nebst anwendungen. Acta math. 54, 117-176 (1929) · Zbl 56.0343.03 [2] Guo, D.; Sun, J.: Nonlinear integral equations. (1987) [3] Krasnoselskii, M. A.: Topological methods in the theory of nonlinear integral equations. (1964) [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) · Zbl 0661.47045 [8] Deimling, K.: Nonlinear functional analysis. (1985) · 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)