Third-order nonlocal problems with sign-changing nonlinearity on time scales
Date
2007-01-27
Authors
Anderson, Douglas R.
Tisdell, Christopher
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
We are concerned with the existence and form of positive solutions to a nonlinear third-order three-point nonlocal boundary-value problem on general time scales. Using Green's functions, we prove the existence of at least one positive solution using the Guo-Krasnoselskii fixed point theorem. Due to the fact that the nonlinearity is allowed to change sign in our formulation, and the novelty of the boundary conditions, these results are new for discrete, continuous, quantum and arbitrary time scales.
Description
Keywords
boundary value problem, time scale, three-point, green's function
Citation
Anderson, D. R., & Tisdell, C. C. (2007). Third-order nonlocal problems with sign-changing nonlinearity on time scales. <i>Electronic Journal of Differential Equations, 2007</i>(19), pp. 1-12.
Rights
Attribution 4.0 International