Geodesic
Semi-regular solutions of integral equations with discontinuous nonlinearities
Matematičeskie zametki, Tome 116 (2024) no. 1, pp. 109-121

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We study integral equations with discontinuous nonlinearities in Lebesgue spaces. Using the variational method, based on the concept of a quasipotential operator, we establish a theorem on the existence of semi-regular solutions. For equations with a parameter, a theorem on the existence of nontrivial semi-regular solutions for sufficiently large parameter values is obtained. An example of an applied problem for which the conditions of these theorems are satisfied is given.
Keywords: integral equation, discontinuous nonlinearity, parameter, semi-regular solution, variational method. 
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     author = {V. N. Pavlenko and D. K. Potapov},
     title = {Semi-regular solutions of integral equations with discontinuous nonlinearities},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2024_116_1_a7/}
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V. N. Pavlenko; D. K. Potapov. Semi-regular solutions of integral equations with discontinuous nonlinearities. Matematičeskie zametki, Tome 116 (2024) no. 1, pp. 109-121. http://geodesic.mathdoc.fr/item/MZM_2024_116_1_a7/