Exact boundary behavior of positive large solutions of a nonlinear Dirichlet problem
| Autor: | Sonia Ben Othman, Bilel Khamessi |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Dirichlet problem
Continuous function (set theory) Applied Mathematics 010102 general mathematics Boundary (topology) Function (mathematics) 01 natural sciences 010101 applied mathematics Combinatorics Nonlinear system Bounded function Domain (ring theory) Boundary value problem 0101 mathematics Analysis Mathematics |
| Zdroj: | Nonlinear Analysis. 187:307-319 |
| ISSN: | 0362-546X |
| DOI: | 10.1016/j.na.2019.05.001 |
| Popis: | In this paper, we investigate the exact asymptotic behavior of positive solution to the following singular boundary value problem Δ u = b ( x ) f ( u ) , x ∈ Ω , u > 0 in Ω , u | ∂ Ω = + ∞ , where Ω is a C 2 -bounded domain in R N , ( N ≥ 3 ), f ∈ C 1 ( ( 0 , ∞ ) , ( 0 , ∞ ) ) is nondecreasing on ( 0 , ∞ ) and b is a function in C l o c γ ( Ω ) , ( 0 γ 1 ) such that there exist b 1 , b 2 > 0 satisfying for each x ∈ Ω , 0 b 1 = lim d ( x ) ⟶ 0 inf b ( x ) h ( d ( x ) ) ≤ lim d ( x ) ⟶ 0 sup b ( x ) h ( d ( x ) ) = b 2 ∞ , where d ( x ) = d i s t ( x , ∂ Ω ) and h ( t ) ≔ c t − λ exp ∫ t η z ( s ) s d s , η > d i a m ( Ω ) , λ ≤ 2 such that z is a continuous function on [ 0 , η ] with z ( 0 ) = 0 . |
| Databáze: | OpenAIRE |
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