Existence of three solutions for partial discrete Dirichlet boundary value problems containing ψ-Laplacian

Using variational methods and critical point theory, this paper investigates parameter intervals that guarantee the existence of at least three solutions for a new class of partially discrete Dirichlet boundary value problems involving the ψ-Laplacian. We also determine parameter regimes under which the norms of these solutions are bounded above by a prescribed positive constant. Furthermore, by employing the strong maximum principle, we show that under suitable assumptions the problem admits at least two and in certain cases three positive solutions. Finally, two illustrative examples are provided to substantiate the theoretical results.