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Let f : R? → R a continuous function such that f(tx,ty) = tª f (x,y) for some a > -2, all (x,y) e R² and t > 0. Prove that there exists a vector e R? of norm one such that 27 JJ f(x, y) a + 2 (§)Rª+2 BR(0,0) where BR(0,0) = {(x, y) : ||(x, y)|| < R}.

Let f : R? → R a continuous function such that f(tx,ty) = tª f (x,y) for some a > -2, all (x,y) e R² and t > 0. Prove that there exists a vector e R? of norm one such that 27 JJ f(x, y) a + 2 (§)Rª+2 BR(0,0) where BR(0,0) = {(x, y) : ||(x, y)|| < R}.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let f : R? → R a continuous function such that f(tx,ty) = tª f (x,y) for some a > -2, all (x,y) e R² and t > 0. Prove that there exists a vector e R? of norm one such that 27 JJ f(x, y) a + 2 (§)Rª+2 BR(0,0) where BR(0,0) = {(x, y) : ||(x, y)|| < R}.
Transcribed Image Text:Let f : R? → R a continuous function such that f(tx,ty) = tª f (x,y) for some a > -2, all (x,y) e R² and t > 0. Prove that there exists a vector e R? of norm one such that 27 JJ f(x, y) a + 2 (§)Rª+2 BR(0,0) where BR(0,0) = {(x, y) : ||(x, y)|| < R}.
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