A Brézis–Oswald-Type Result for the Fractional (r, q)-Laplacian Problems and Its Application - Yun-Ho Kim; In Hyoun Kim (Fractal and Fractional)
This study derives the uniqueness of positive solutions to Brézis–Oswald-type problems involving the fractional <semantics>(r,q)</semantics>-Laplacian operator and discontinuous Kirchhoff-type coefficients. The Brézis–Oswald-type result and Ricceri’s abstract global minimum principle are critical tools in identifying this uniqueness. We consider an eigenvalue problem associated with fractional <semantics>(r,q)</semantics>-Laplacian problems to confirm the existence of a positive solution for our problem without the Kirchhoff coefficient. Moreover, we establish the uniqueness result of the Brézis–Oswald type by exploiting a generalization of the discrete Picone inequality.