Multiple solutions for boundary value problems of a discrete generalized Emden-Fowler equation (Q1049238)

The authors consider the following boundary value problem for a discrete Emden-Fowler equation \[ \Delta [p_k\Delta u_{k-1}]+ q_k u_k+ f(k,u_k)= 0, \quad u_0= u_N , \quad p_0\Delta u_0= p_N \Delta u_N, \] and show the existence of at least \(2N\) solutions, if the function \(s\mapsto f(k,s)\) is odd and fulfills a certain growth condition for \(s \to 0\).