Multiple Solutions and Eigenvalues for Third-Order Right Focal Boundary Value Problems

We are concerned with the right focal boundary value problem x t = f t x t t1 ≤ t ≤ t3 x t1 = x t2 = x t3 = 0 and the associated eigenvalue problem x t = λa t f x t with the same boundary conditions. Under various assumptions on f , a, and λ we establish intervals of the parameter λ which yield the existence of a positive solution of the eigenvalue problem. By placing certain restrictions on the nonlinearity, we prove the existence of at least one, at least two, at least three, and infinitely many positive solutions of the boundary value problem by applying some known fixedpoint theorems as well as some recent generalizations of these fixed-point theorems.