Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl

PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
• # Artykuł - szczegóły

## Annales Polonici Mathematici

2013 | 109 | 1 | 93-107

## Existence and nonexistence of solutions for a singular elliptic problem with a nonlinear boundary condition

EN

### Abstrakty

EN
We consider the existence and nonexistence of solutions for the following singular quasi-linear elliptic problem with concave and convex nonlinearities:
⎧ $-div(|x|^{-ap} |∇u|^{p-2} ∇u) + h(x)|u|^{p-2}u = g(x)|u|^{r-2}u$, x ∈ Ω,

⎩ $|x|^{-ap}|∇u|^{p-2} ∂u/∂ν = λf(x)|u|^{q-2}u$, x ∈ ∂Ω,
where Ω is an exterior domain in $ℝ^N$, that is, $Ω = {ℝ^N}∖D$, where D is a bounded domain in $ℝ^N$ with smooth boundary ∂D(=∂Ω), and 0 ∈ Ω. Here λ > 0, 0 ≤ a < (N-p)/p, 1 < p< N, ∂/∂ν is the outward normal derivative on ∂Ω. By the variational method, we prove the existence of multiple solutions. By the test function method, we give a sufficient condition under which the problem has no nontrivial nonnegative solutions.

93-107

wydano
2013

### Twórcy

autor
• College of Science, Hohai University, Nanjing 210098, P.R. China
• Science and Information College, Qingdao Agricultural University, Qingdao 266109, P.R. China
autor
• College of Science, Hohai University, Nanjing 210098, P.R. China