Optimization for Nonlinear Integral Equations with Boundary Singularities
Keywords:
Optimization problem , nonlinear equations, boundary singularity, boundedness, continuity, uniform continuity, Holder’s inequality, problem solvability, contraction mapping methodAbstract
This article investigates an optimization problem for objects described by nonlinear integral equations with a singularity at the boundary of integration. Within the framework of the theorem, possibly weaker conditions were imposed, which allow for the verification of the kernel of the integrand and the nonlinear part. The results obtained enable a direct approximation of the solution to the singular nonlinear integral equation and, among the set of solutions, the identification of a control that ensures the minimal value of the function.
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