Multiplicity of nonnegative solutions for semilinear Robin problems involving sign‐changing nonlinearities

Key Points

• The study aims to explore the existence and multiplicity of nonnegative solutions in semilinear Robin problems with sign-changing nonlinearities.
• Investigated Robin problems defined over smooth bounded domains.
• Assumed locally Lipschitz functions that exhibit sign changes across specific intervals.
• Analyzed limiting behaviors of solution sets transitioning to associated Neumann and Dirichlet problems.
• Established the existence of two nonnegative solutions for sufficiently large parameters in the Robin problem.
• Demonstrated that the solution set degenerates into that of the Neumann problem as parameters approach a limit.
• Showed that the solution set approaches that of the Dirichlet problem under different limiting conditions.