Uniqueness of solutions to an Abel type nonlinear integral equation on the half line

• Autorzy: Wojciech Mydlarczyk
• Języki publikacji: EN

Abstrakty

EN

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 metrics.

Słowa kluczowe

EN

Nonlinear Volterra integral equations; Integral inequalities; Nontrivial solutions; Uniqueness of solution; Generalized Osgood condition

Kategorie tematyczne

• 45G10: Other nonlinear integral equations
• 45M20: Positive solutions
• 45D05: Volterra integral equations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 6
• Strony: 1995-2002

Daty

wydano

2012-12-01

online

2012-10-12

Twórcy

autor

Wojciech Mydlarczyk

• Institute of Mathematics and Computer Science, Technical University of Wrocław, Wybrzeże Wyspiańskiego 27, 50-367, Wrocław, Poland

Bibliografia

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• [9] Mydlarczyk W., Okrasinski W., Positive solutions to a nonlinear Abel type integral equation on the whole line, Comput. Math. Appl., 2001, 41(7-8), 835–842 http://dx.doi.org/10.1016/S0898-1221(00)00323-0[Crossref]
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Identyfikatory

DOI

10.2478/s11533-012-0104-9