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Fixed point results for compact maps on closed subsets of Fréchet spaces and applications to differential and integral equations. (English) Zbl 1026.47047

Building on a continuation principle of Leray-Schauder-Nagumo type, the author proves a fixed point theorem for compact maps on closed subsets of Fréchet spaces. Applications to initial value problems on unbounded intervals, infinite systems of differential equations, and Fredholm integral equations are given as well.

MSC:

47H10 Fixed-point theorems
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
45B05 Fredholm integral equations
34G20 Nonlinear differential equations in abstract spaces
45G10 Other nonlinear integral equations
47N20 Applications of operator theory to differential and integral equations
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Full Text: Euclid