On the discrete boundary value problem for anisotropic equation

作者：Galewski Marek^*; Glab Szymon

来源：Journal of Mathematical Analysis and Applications, 2012, 386(2): 956-965.

DOI：10.1016/j.jmaa.2011.08.053

• Anisotropic difference equation
• Three critical point theorem
• Mountain pass lemma
• Direct variational method

In this paper we consider the discrete anisotropic boundary value problem using critical point theory. Firstly we apply the direct method of the calculus of variations and the mountain pass technique in order to reach the existence of at, least one nontrivial solution. Secondly we derive some version of a discrete three critical point theorem which we apply in order to get the existence of at least two nontrivial solutions.

• 出版日期2012-2-15