Multiple and particular solutions of a second order discrete boundary value problem with mixed periodic boundary conditions

Abstract

In this paper, a second order discrete boundary value problem with a pair of mixed periodic boundary conditions is considered. Sufficient conditions on the existence of multiple solutions are obtained by using the critical point theory. Necessary conditions for a particular solution subject to pre-defined criteria are also investigated. Examples are given to illustrate the applications of the results as well.

Keywords

• discrete boundary value problem
• mixed periodic boundary conditions
• variational methods
• mountain pass lemma
• lagrange multiplier