Nontrivial solutions to nonlinear Volterra equations
W. Okrasinski (1989)
Extracta Mathematicae
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W. Okrasinski (1989)
Extracta Mathematicae
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W. Okrasinski (1989)
Extracta Mathematicae
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W. Okrasinski (1993)
Extracta Mathematicae
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Wojciech Mydlarczyk (2012)
Open Mathematics
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We 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...
W. Mydlarczyk (1991)
Annales Polonici Mathematici
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Mydlarczyk, W. (2001)
Journal of Inequalities and Applications [electronic only]
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W. Okrasinski (1989)
Extracta Mathematicae
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Jesús M. Fernández Castillo, W. Okrasinski (1991)
Extracta Mathematicae
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In mathematical models of some physical phenomena a new class of nonlinear Volterra equations appears ([5],[6]). The equations belonging to this class have u = 0 as a solution (trivial solution), but with respect to their physical meaning, nonnegative nontrivial solutions are of prime importance.