Existence and uniqueness of fixed points of an integral operator of Hammerstein type. (English. Russian original) Zbl 1490.45014
Theor. Math. Phys. 208, No. 3, 1228-1238 (2021); translation from Teor. Mat. Fiz. 208, No. 3, 440-451 (2021).
The author discusses the fixed points of a nonlinear integral operator of Hammerstein type. Here, such an operator is neither compact nor contracting. Therefore, some well-known theorems such as the Schauder fixed-point theorem and the Banach fixed-point theorem do not apply.
The existence of fixed points of nonlinear integral operators of Hammerstein type has been established by other authors, and the author of the present paper establishes their uniqueness under certain conditions. Moreover, he applies the results to several interesting examples such as the antiferromagnetic and ferromagnetic Ising models.
Reviewer: Shuji Watanabe (Maebashi)
MSC:
| 45P05 | Integral operators |
| 47H10 | Fixed-point theorems |
| 47N20 | Applications of operator theory to differential and integral equations |
Keywords:
Hammerstein integral operator; positive fixed point; existence; uniqueness; cone; normal coneReferences:
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