Trace operator and a nonlinear boundary value problem in a new space

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• 作者：Hee Chul Pak (1)
  Young Ja Park (2)
  
  1. Department of Mathematics ; Dankook University ; Anseo-Dong 29 ; Cheonan ; Chungnam ; 330-714 ; Republic of Korea
  2. Department of Mathematics ; Hoseo University ; Asan ; Chungnam ; 336-795 ; Republic of Korea
  
• 关键词：30E25 ; 35A01 ; 46E35 ; 42B35 ; trace operator ; boundary value problem ; function space ; non ; existence
• 刊名：Boundary Value Problems
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：2014
• 期：1
• 全文大小：1,101 KB
• 参考文献：1. Pak, H-C (2011) Existence of solutions for a nonlinear elliptic equation with general flux term. Fixed Point Theory Appl. 2011: CrossRef
  2. do Carmo, M (1976) Differential Geometry of Curves and Surfaces. Prentice Hall, Englewood Cliffs
  3. Adams, R (2003) Sobolev Spaces. Academic Press, Amsterdam
  
• 刊物主题：Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations; Analysis; Approximations and Expansions; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1687-2770

文摘

We develop a new function space and discuss trace operator on the same genealogical spaces. We also prove that the nonlinear boundary value problem with Dirichlet condition: \(-\Delta u= f(|u|) \operatorname{sgn} u \) in the given domain, \(u = 0\) on the boundary, possesses only a trivial solution if \(f\) obeys the slope condition: \(\alpha'(x) > \frac{2n}{n-2} \frac{\alpha(x)}{x}\) , where \(\alpha\) is the anti-derivative of \(f\) with \(\alpha(0) = 0\) .