The Method of upper and lower solutions for second-order non-homogeneous two-point boundary-value problem
Texas State University-San Marcos, Department of Mathematics
This paper studies the existence and uniqueness of solutions for a type of second-order two-point boundary-value problem depending on the first-order derivative through a non-linear term. By constructing a special cone and using the upper and lower solutions method, we obtain the sufficient conditions of the existence and uniqueness of solutions, and a monotone iterative sequence solving the boundary-value problem. An error estimate formula is also given under the condition of a unique solution.
upper and lower solutions, cone, monotone iterative method
Jia, M., & Liu, X. (2007). The Method of upper and lower solutions for second-order non-homogeneous two-point boundary-value problem. <i>Electronic Journal of Differential Equations, 2007</i>(116), pp. 1-10.
Attribution 4.0 International