The Existence of Nontrivial Solutions for a Class of Volterra Equations with Smooth Kernels.
W. Mydlarczyk (1992)
Mathematica Scandinavica
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We consider the following Volterra equation: (1) u(x) = ∫0 x k(x-s) g(u(s)) ds, where, k: [0, δ0] → R is an increasing absolutely continuous function such that k(0) = 0 g: [0,+ ∞) → [0,+ ∞) is an increasing absolutely continuous function such that g(0) = 0 and g(u)/u → ∞ as u → 0+ (see [3]). Let us note that (1) has always...
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