| | |
Summary: DISCRETE THIRD-ORDER THREE-POINT RIGHT FOCAL
BOUNDARY VALUE PROBLEMS
DOUGLAS R. ANDERSON
Abstract. We are concerned with the discrete right-focal boundary value
problem 3x(t) = f(t, x(t + 1)), x(t1) = x(t2) = 2x(t3) = 0, and the
eigenvalue problem 3x(t) = a(t)f(x(t + 1)) with the same boundary condi-
tions, where t1 < t2 < t3. Under various assumptions on f, a and we prove
the existence of positive solutions of both problems by applying a fixed point
theorem.
1. Introduction
In this paper, we are concerned with the existence of positive solutions to the
discrete third-order three-point eigenvalue problem:
3
x(t) = a(t)f(x(t + 1)) for all t [t1, t3 - 1] (1)
x(t1) = x(t2) = 2
x(t3) = 0,
and the boundary value problem
3
x(t) = f(t, x(t + 1)) for all t [t1, t3 - 1] (2)
x(t1) = x(t2) = 2
|
