On quasimonotone increasing homeomorphisms |
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Authors: | Gerd Herzog |
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Institution: | (1) College of Automation, Chongqing University, 400044 Chongqing, China;(2) Department of Computer Science, Chongqing Education College, 400067 Chongqing, China |
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Abstract: | Let f ? C(\Bbb Rn,\Bbb Rn) f\in C(\Bbb R^n,\Bbb R^n) be quasimonotone increasing such that Y(f(y)-f(x)) £ -c Y(y-x) (x << y) \Psi (f(y)-f(x)) \!\le -c \Psi (y-x) (x\ll y) for a linear and strictly positive functional Y \Psi and c > 0. We prove that f is a homeomorphism with decreasing and Lipschitz continuous inverse and we prove the global asymptotic stability of the equilibrium solution of x¢=f(x) x'=f(x) . |
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