Multiple positive solutions of singular and nonsingular discrete problems via variational methods
The authors use the critical point theory to obtain the existence of multiple positive solutions of the discrete boundary value problem \[ \Delta ^{2}y(k-1)+f(k,y(k))=0,\;k\in \{1,...,T\},\quad y(0)=0=y(T+1), \] where \(T\) is a positive integer, \(\Delta y(k)=y(k+1)-y(k)\) is the forward difference operator and \(f\in C(\{1,...,T\}\times [ 0,\infty );\mathbb{R}) \) is a given function with some specific properties.
scientific article; zbMATH DE number 2092993