Existence and stability of solutions for a Sea-Breeze flow model

In this paper, we investigate a second-order ordinary differential equation that describes the phenomenon of sea breeze flow under specific geographical and viscosity conditions. By considering the forcing term in linear function form, we present the explicit solution and stability, which primarily include local asymptotic stability and semi-Ulam–Hyers stability. Then, we establish the criteria for the existence and uniqueness of solutions to the equation for various nonlinear forcing terms, including Lipschitz-type nonlinear and general nonlinear.