Extension of the example by Moore-Nehari

Armands Gritsans, Felix Sadyrbaev
  • Tatra Mountains Mathematical Publications, January 2015, De Gruyter
  • DOI: 10.1515/tmmp-2015-0024

Multiple solutions in a boundary value problem

What is it about?

It is about the second order ordinary differential equation with a cubic non-linearity that has a coefficient depending on time and this coefficient is a piece-wise (step) function.

Why is it important?

It provides relatively simple example of a problem that has countable number of solutions. Previously it was believed that this problem has three solutions.

Perspectives

Felix Sadyrbaev

Examples can be provided of problems of classical calculus of variations that have multiple minimizers as well as maximizers.

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http://dx.doi.org/10.1515/tmmp-2015-0024

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