一类推广的二变量和差分不等式及其在初边值问题中的应用

Abstract

Abstract:

In this paper, we establish a general form of sum-difference inequality in two variables, which contains both a nonconstant term outside the sums and k terms of nonlinear 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 in the work of Cheung W S (2006) and Wang W S (2008). Furthermore, we apply our result to a boundary value problem of a partial difference equation for boundedness, uniqueness and continuous dependence.

Key words: Sum-difference inequality, Monotonization, Stronger nondecreasing, Boundedness

CLC Number:

39A10

WANG Wu-Sheng, LI Zi-Zun, ZHOU Xiao-Liang. A New Generalized Sum-Difference Inequality with Two Variables and Applications to BVP[J].Acta mathematica scientia,Series A, 2013, 33(2): 340-353.

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A New Generalized Sum-Difference Inequality with Two Variables and Applications to BVP

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