Positive solutions and eigenvalues of nonlocal boundary-value problems
Texas State University-San Marcos, Department of Mathematics
We study the ordinary differential equation x'' + λα(t)ƒ(x) = 0 with the boundary conditions x(0) = 0 and x'(1) = ∫¹η x'(s)dg(s). We characterize values of λ for which boundary-value problem has a positive solution. Also we find appropriate intervals for λ so that there are two positive solutions.
Nonlocal boundary-value problems, Positive solutions, Eigenvalues, Fixed point theorem in cones
Chu, J., & Zhou, Z. (2005). Positive solutions and eigenvalues of nonlocal boundary-value problems. <i>Electronic Journal of Differential Equations, 2005</i>(86), pp. 1-9.