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On the existence and non-existence of positive solutions for a class of singular infinite semipositone problems
- Source :
- Lobachevskii Journal of Mathematics. 34:207-211
- Publication Year :
- 2013
- Publisher :
- Pleiades Publishing Ltd, 2013.
-
Abstract
- In this paper we consider the existence and non-existence of positive solutions of singular nonlinear semipositone problem of the form $$\left\{ \begin{gathered} - div(|x|^{ - ap} |\nabla u|^{p - 2} \nabla u) = \lambda |x|^{ - (a + 1)p + b} (f(u) - \frac{1} {{u^\alpha }}),x \in \Omega , \hfill \\ u = 0,x \in \partial \Omega , \hfill \\ \end{gathered} \right. $$ where Ω is a bounded smooth domain of RN with 0 ∈ Ω, 1 < p < N, 0 ≤ a < \(\tfrac{{N - p}} {p} \), α ∈ (0, 1), and b, λ are positive parameters. Here f : (0, ∞) → (0, ∞) is C2 function. Our aim in this paper is to establish non-existence of positive solution for λ near zero and existence of positive solution for λ large. We use the method of sub-super solutions to establish our existence result.
Details
- ISSN :
- 18189962 and 19950802
- Volume :
- 34
- Database :
- OpenAIRE
- Journal :
- Lobachevskii Journal of Mathematics
- Accession number :
- edsair.doi...........b82b1d448d2fb4a6a46d8e2f0e5d16f1