By Günther Windisch
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33) is a nonsingular M-matrix. This assumption implies 0 for k=1, •• ,p. Further, let n ~ 2p+1 and ak~ r.. e. 2 4 Windisch, Analysis and Ae ~ 0, • 0. 49 In the following we need Jensen's inequality, see Ca]. Let (a,b) be an arbitrary interval. 34) ranges over a well defined index set {k}. , if 'f" (x) < 0 for each xE(a,b). and xi • ih, i • -p, ••• To apply Jensen's inequality, we seth • •• ,n+p+1. Putting a • x_P and b • Xn+p+ 1 ' let "(x) ~ c2 (a,b) be a function with the following properties!
Xi .. ih. First of all, we consider the following model problem. 1. Q u( 1 ) • u 1 • Suppose that b(x) is a bounded function in Sl • Then any c 2 solution u(x) • const satisfies the boundary maximum principle min {u0 ,u1} ' u(x) see [22}. 1.
2 4 Windisch, Analysis and Ae ~ 0, • 0. 49 In the following we need Jensen's inequality, see Ca]. Let (a,b) be an arbitrary interval. 34) ranges over a well defined index set {k}. , if 'f" (x) < 0 for each xE(a,b). and xi • ih, i • -p, ••• To apply Jensen's inequality, we seth • •• ,n+p+1. Putting a • x_P and b • Xn+p+ 1 ' let "(x) ~ c2 (a,b) be a function with the following properties! 35a) 0 for each (a, b). 35b) x~ Examples of such functions 'f(x) are easily available, for instance, we can choose cp(x) = - x 2 + c, c sufficiently large.