TY - JOUR

T1 - Semi-Regular Solutions of Integral Equations with Discontinuous Nonlinearities

AU - Pavlenko, V.N.

AU - Potapov, D.K.

PY - 2024/8/1

Y1 - 2024/8/1

N2 - Abstract: 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.

AB - Abstract: 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.

KW - discontinuous nonlinearity

KW - integral equation

KW - parameter

KW - semi-regular solution

KW - variational method

UR - https://www.mendeley.com/catalogue/611ec304-a530-3c61-a039-68234a5fd63a/

U2 - 10.1134/S0001434624070083

DO - 10.1134/S0001434624070083

M3 - Article

VL - 116

SP - 93

EP - 103

JO - Mathematical Notes

JF - Mathematical Notes

SN - 0001-4346

IS - 1-2

ER -