Eigenvalue problems for p-Laplacian dynamic equations on time scales
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In this paper, we are concerned with the following eigenvalue problems of m-point boundary value problem for p-Laplacian dynamic equation on time scales <수식> where φ_p(u) = |u|^p−2u, 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.
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 scales <수식> where φ_p(u) = |u|^p−2u, 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.
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