EIGENVALUE PROBLEMS FOR p-LAPLACIAN DYNAMIC EQUATIONS ON TIME SCALES

Abstract

Abstract. In this paper, we are concerned with the following eigenvalue problems of m-point boundary value problem for p-Laplacian dynamic equation on time scaleswhere ϕ p (u) = |u| p−2 u, p > 1 and λ > 0 is a real parameter. Under certain assumptions, some new results on existence of one or two positive solution and nonexistence are obtained for λ evaluated in different intervals. Our work develop and improve many known results in the literature even for the continual case. In doing so the usual restriction that f 0 = lim u→0 + f (u)/ϕ p (u) and f ∞ = lim u→∞ f (u)/ϕ p (u) exist is removed. As an applications, an example is given to illustrate the main results obtained.