This paper investigates the existence and multiplicity of positive solutions for a class of nonlinear boundary-value problem of second-order differential equations with integral boundary conditions in ordered Banach spaces. The arguments are based upon a specially constructed cone and the fixed point theory in a cone for strict set contraction operators. The nonexistence of a positive solution is also studied.
In this paper, some new discrete inequalities in two independent variables which provide explicit bounds on unknown functions are established. The inequalities given here can be used as tools in the qualitative theory of certain finite difference equations.
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