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Asymptotic properties of solutions of semilinear second-order elliptic equations in cylindrical domains.
- Source :
- Journal of Mathematical Sciences; May2006, Vol. 135 Issue 1, p2666-2674, 9p
- Publication Year :
- 2006
-
Abstract
- The equations under consideration have the following structure: where 0 < x <subscript>n</subscript> < ∞, ( x <subscript>1</subscript>, ..., x <subscript> n−1</subscript>) ∈ Ω, Ω is a bounded Lipschitz domain, $$f(0,x_n ) \equiv 0,\tfrac{{\partial f}}{{\partial u}}(0,x_n ) \equiv 0$$ is a function that is continuous and monotonic with respect to u, and all coefficients are bounded measurable functions. Asymptotic formulas are established for solutions of such equations as x <subscript>n</subscript> → + ∞; the solutions are assumed to satisfy zero Dirichlet or Neumann boundary conditions on ∂Ω. Previously, such formulas were obtained in the case of a <subscript>ij</subscript>, a<subscript>i</subscript> depending only on ( x <subscript>1</subscript>, ..., x <subscript> n−1</subscript>). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10723374
- Volume :
- 135
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Journal of Mathematical Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 20360296
- Full Text :
- https://doi.org/10.1007/s10958-006-0136-4