The authors study a one-dimensional -Laplacian equation of the form
together with the boundary conditions
The numbers belong to ; is Carathéodory in ; and are continuous and nondecreasing in the -variables; is an odd homeomorphism of .
They introduce the notion of coupled lower and upper solutions as a pair of functions of satisfying, in addition to the standard differential inequalities, boundary inequalities that make sense by virtue of a Nagumo condition that verifies with respect to the pair , . Under these conditions, they show that the problem (1)-(2) has at least one solution between and .
Several consequences follow. In particular, if
with and is nondecreasing in , there exists a unique solution. Also, an application is given to the existence of radial solutions in an annulus of the equation
Here is an increasing homeomorphism of , the are nonnegative, and .