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On the Number of Positive Solutions to a Class of Integral Equations
By using the complete discrimination system for polynomials, we study the
number of positive solutions in {\small } to the integral equation
{\small }, where {\small
} are continuous functions on {\small }, {\small } is
a positive integer. We prove the following results: when {\small },
either there does not exist, or there exist infinitely many positive solutions
in {\small }; when {\small }, there exist at least {\small 1},
at most {\small } positive solutions in {\small }. Necessary and
sufficient conditions are derived for the cases: 1) {\small }, there
exist positive solutions; 2) {\small }, there exist exactly {\small
} positive solutions. Our results generalize the
existing results in the literature, and their usefulness is shown by examples
presented in this paper.Comment: 9 page
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