Extension of the example by Moore – Nehari

Abstract

R. Moore and Z. Nehari developed the variational
theory for superlinear boundary value problems of the form

$  x'' = -p(t) |x|^{2 \varepsilon} x, x (a) = 0 = x (b) $, where $ \varepsilon > 0  $

and

$ p(t)  $

is a positive
continuous function. They constructed simple example of the equation
considered in the interval

$ [0; b] $

so that the problem had three
positive solutions. We show that this example can be extended so
that the respective BVP has infinitely many groups of solutions with
a presribed number of zeros.