Eigenvalues and symmetric positive solutions for a three-point boundary-value problem
Texas State University-San Marcos, Department of Mathematics
In this paper, we consider the second-order three-point boundary-value problem u′′(t) + ƒ(t, u, u′, u′′) = 0, 0 ≤ t ≤ 1, u(0) = u(1) = αu(η) Under suitable conditions and using Schauder fixed point theorem, we prove the existence of at least one symmetric positive solution. We also study the existence of positive eigenvalues for this problem. We emphasis the highest-order derivative occurs nonlinearly in our problem.
Symmetric positive solution, Three-point boundary-value problem, Schauder fixed point theorem, Eigenvalue
Sun, Y. (2005). Eigenvalues and symmetric positive solutions for a three-point boundary-value problem. <i>Electronic Journal of Differential Equations, 2005</i>(127), pp. 1-7.