On Robin problems with infinite‐point BCs

Abstract

We study semilinear equations with Robin‐type infinite‐point boundary conditions, where the boundary conditions depend nonlocally on the solution at infinitely many interior points. To overcome the difficulties arising from the lack of guaranteed variational structure in these models, we establish mappings that correspond to the boundary conditions. Through a combination of asymptotic analysis and fixed‐point arguments, we prove the existence of solutions under specific assumptions. This approach is novel in related research.