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

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: − Δ u = f ( | u | ) sgn u in the given domain, u = 0 on the boundary, possesses only a trivial solution if f obeys the slope c...

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Bibliographic Details
Published in:Boundary value problems 2014-09, Vol.2014 (1), p.1-13, Article 153
Main Authors: Pak, Hee Chul, Park, Young Ja
Format: Article
Language:English
Subjects:
Analysis
Approximations and Expansions
Boundaries
Boundary value problems
Difference and Functional Equations
Dirichlet problem
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinearity
Operators
Ordinary Differential Equations
Partial Differential Equations
Slopes
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Summary: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: − Δ u = f ( | u | ) sgn u in the given domain, u = 0 on the boundary, possesses only a trivial solution if f obeys the slope condition: α ′ ( x ) > 2 n n − 2 α ( x ) x , where α is the anti-derivative of f with α ( 0 ) = 0 .
ISSN:1687-2770
1687-2770
DOI:10.1186/s13661-014-0153-z