Three Nontrivial Solutions for Second-Order Partial Difference Equation via Morse Theory - Yuhua Long; Huan Zhang (Journal of Function Spaces)
In the present paper, we consider a second-order nonlinear partial difference equation with Dirichlet boundary conditions. Applying variational method together with the Morse theory, we establish a criterion to obtain at least three nontrivial solutions. An example is also elaborated to demonstrate our main result.