Abstract
AbstractThis paper focuses on second-order differential equations involving causal operators with nonlinear two-point boundary conditions. By applying the monotone iterative technique in the presence of upper and lower solutions, with a new comparison theorem, we obtain the existence of extremal solutions. This is an extension of classical theory of second-order differential equations. Finally, we present two examples to show the usefulness of our results.
Funder
National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Reference19 articles.
1. Agarwal, R.P., Franco, D., O’Regan, D.: Singular boundary value problems for first and second order impulsive differential equations. Aequ. Math. 69(1–2), 83–96 (2005)
2. Campbell, J.: The smm model as a boundary value problem using the discrete diffusion equation. Theor. Popul. Biol. 72(4), 539–546 (2007)
3. Chen, L., Sun, J.: Boundary value problem of second order impulsive functional differential equations. J. Math. Anal. Appl. 323(1), 708–720 (2006)
4. Corduneanu, C.: Boundedness of solutions for a second order differential equation with causal operators. Nonlinear Stud. 18(2), 135–139 (2011)
5. Drici, Z., Mcrae, F.A., Devi, J.V.: Monotone iterative technique for periodic boundary value problems with causal operators. Nonlinear Anal. 64(6), 1271–1277 (2006)