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A study of second-order q-difference equations with boundary conditions
Advances in Difference Equations
This paper studies a boundary value problem of nonlinear second-order q-difference equations with non-separated boundary conditions. As a first step, the given boundary value problem is converted to an equivalent integral operator equation by using the q-difference calculus. Then the existence and uniqueness of solutions of the problem is proved via the resulting integral operator equation by means of Leray-Schauder nonlinear alternative and some standard fixed point theorems. Our approach isdoi:10.1186/1687-1847-2012-35 fatcat:z4almqghpvcf7f4wtcr3o5qp5m