A Generalized Sum-Difference Inequality and Applications to Partial Difference Equations
نویسندگان
چکیده
We establish a general form of sum-difference inequality in two variables, which includes both two distinct nonlinear sums without an assumption of monotonicity and a nonconstant term outside the sums. We employ a technique of monotonization and use a property of stronger monotonicity to give an estimate for the unknown function. Our result enables us to solve those discrete inequalities considered by Cheung and Ren 2006 . Furthermore, we apply our result to a boundary value problem of a partial difference equation for boundedness, uniqueness, and continuous dependence.
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