Two existence results are presented for second-order discrete boundary value problems. The first result is based on the notion of upper and lower solutions and the second result is based on the discrete Gelfand problem.

An existence principle is established for Delta u + f(t, u) = 0 on Omega, u = 0 on partial derivative Omega. Our theory relies on a fixed point result for weakly sequentially continuous and weakly compact maps.

We extend a fixed-point theorem of Reinermann [1] for the sum of two operators. Our results are then used to establish new existence results for differential equations in Banach spaces.

We present continuation results for operators between locally convex linear topological spaces. These results will then be applied to obtain existence principles for differential equations on semi-infinite intervals.

We study superlinear boundary value problems for a discrete system which in particular includes the prototype equation x(k + 1) = f(k,x(k)), equations with finite as well as infinite delays, equations of neutral type, and ...