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Askhabov, S. N.

Nonlinear integral equations with potential-type kernels on a segment. (English. Russian original) Zbl 1471.45004

J. Math. Sci., New York 235, No. 4, 375-391 (2018); translation from Sovrem. Mat., Fundam. Napravl. 60, 5-22 (2016).
Summary: We study various classes of nonlinear equations containing operators of potential type (Riesz potential). By the method of monotone operators in the Lebesgue spaces of real-valued functions \(L_p(a, b)\) we prove global theorems on the existence, uniqueness, estimates, and methods of construction of their solutions. We present applications that illustrate the results obtained.

MSC:

45G10 Other nonlinear integral equations
47H05 Monotone operators and generalizations

Keywords:

Riesz potential; monotone operators; Lebesgue spaces
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\textit{S. N. Askhabov}, J. Math. Sci., New York 235, No. 4, 375--391 (2018; Zbl 1471.45004); translation from Sovrem. Mat., Fundam. Napravl. 60, 5--22 (2016)
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References:

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