Extension of the example by Moore-Nehari
Armands Gritsans, Felix Sadyrbaev · Tatra Mountains Mathematical Publications · 2015
Abstract R. Moore and Z. Nehari developed the variational theory for superlinear boundary value problems of the form x'' = p(t) |x|2εx, x(a) = 0 = x(b), where ε > 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.