Nonlinear integral equations with potential-type kernels in the nonperiodic case. (English. Russian original) Zbl 1494.45006
J. Math. Sci., New York 263, No. 4, 463-474 (2022); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 170, 3-14 (2019).
Summary: We find conditions under which a generalized potential-type operator acts continuously from a Lebesgue space with a general weight to its dual space and possesses the positivity property. Based on these conditions, we prove the global existence and uniqueness theorems for various classes of nonlinear integral equations of convolution type in real weighted Lebesgue spaces using the method of monotonic (in the Browder-Minty sense) operators. Also we obtain estimates of the norms of solutions, which imply that the corresponding homogeneous equations have only a trivial solution.
MSC:
| 45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
| 45G10 | Other nonlinear integral equations |
| 47J05 | Equations involving nonlinear operators (general) |
Keywords:
positive operator; generalized potential-type operator; monotonic operator; nonlinear integral equationReferences:
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