Dynamics of Partial Differential Equations
Volume 8 (2011)
Positive solutions to the singular p-Laplacian BVPs with sign-changing nonlinearities and higher-order derivatives in Banach spaces on time scales
Pages: 149 – 171
In this paper, in order to establish the existence criteria for positive solutions of a multiple-point Dirichlet-Robin BVPs in Banach spaces on time scales, first we prove a fixed point theorem on monotone operators and the Ascoli-Arzela’s theorem on time scales. Then using the monotone operator method, we explore the existence criteria of positive solutions for a general multiple-point Dirichlet-Robin BVPs in Banach spaces on time scales with the singular sign-changing nonlinearities and higher-order derivatives. Finally an example is illustrated to indicate the application of our main results, which generalize some well-known results in the literature.
boundary value problem, time scales, fixed point, delta derivative, positive solution, partial ordering, p-Laplacian, Ascoli-Arzela’s Theorem
2010 Mathematics Subject Classification
Primary 34B15, 35B09. Secondary 34A12.