Difference and Functional Equations 39
نویسندگان
چکیده
MR2864818 39A05 37B99 Sacker, Robert J. (1-SCA; Los Angeles, CA) An invariance theorem for mappings. (English summary) J. Difference Equ. Appl. 18 (2012), no. 1, 163–166. The following theorem is proved. Theorem 2.1. LetD ⊂ R be a bounded subset and f :D→ R be continuous. Suppose f : ◦ D→ R is injective (one-to-one) and f(∂D)⊂D. If D := R rD has no bounded components, then f(D)⊂D. Here D is the closure of set D, ◦ D is the interior of D, ∂D = D r ◦ D. A simplified application is given to a biological migration-selection model. Vladimir Sh. Burd
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