This paper is concerned with the existence of multiple solutions of the following class of boundary value problems on an unbounded domain
with is a continuous function and is a continuous function such that where is a real constant.
The proofs are based on the method of lower and upper solutions and the theory of topological degree on compact domains. Then, they extend solutions to the unbounded domain with sequential arguments. An example is given. For quantitative contributions on boundary value problems on unbounded domains compare [R. P. Agarwal and D. O’Regan, Infinite interval problems for differential, difference and integral equations. Dordrecht: Kluwer Academic Publishers (2001; Zbl 0988.34002)].