Nonlinear Integral Equations with Potential-Type Kernels in the Nonperiodic Case

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 nonlinea...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 263; no. 4; pp. 463 - 474
Main Author Askhabov, S. N.
Format Journal Article
LanguageEnglish
Published New York Springer US 09.05.2022
Springer
Springer Nature B.V
Subjects
Existence theorems
Integral equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Norms
Uniqueness theorems
45G10
47J05
positive operator
nonlinear integral equation
generalized potential-type operator
monotonic operator
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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.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-05942-5