projective metrics
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2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Wojciech Mydlarczyk

AbstractWe consider a convolution-type integral equation u = k ⋆ g(u) on the half line (−∞; a), a ∈ ℝ, with kernel k(x) = x α−1, 0 < α, and function g(u), continuous and nondecreasing, such that g(0) = 0 and 0 < g(u) for 0 < u. We concentrate on the uniqueness problem for this equation, and we prove that if α ∈ (1, 4), then for any two nontrivial solutions u 1, u 2 there exists a constant c ∈ ℝ such that u 2(x) = u 1(x +c), −∞ < x. The results are obtained by applying Hilbert projective metrics.


1965 ◽  
Vol 71 (5) ◽  
pp. 773-776 ◽  
Author(s):  
Richard Bellman ◽  
Thomas A. Brown

1964 ◽  
Vol 19 (5) ◽  
pp. 49-107 ◽  
Author(s):  
I M Yaglom ◽  
B A Rozenfel'd ◽  
E U Yasinskaya
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