Loading...

On existence, non-existence and blow-up results for a singular semilinear laplacian problem

Bayrami, M ; Sharif University of Technology

531 Viewed
  1. Type of Document: Article
  2. DOI: 10.1007/s40879-017-0129-5
  3. Abstract:
  4. We study the optimal value of p for solvability of the problem [Equation not available: see fulltext.]Here λ, α> 0 , p> 1 , f is a non-negative measurable function and [InlineEquation not available: see fulltext.], N⩾ 3 , is an open bounded domain with smooth boundary such that 0 ∈ Ω. We find the critical threshold exponent p+(λ, α) for solvability of (1) and show that if [InlineEquation not available: see fulltext.], 1 < p< p+(λ, α) and [InlineEquation not available: see fulltext.] for some sufficiently small c0> 0 , then there exists a solution as a limit of solutions to approximating problems. Moreover, for p⩾ p+(λ, α) we show that a complete blow-up phenomenon occurs. © 2017, Springer International Publishing AG
  5. Keywords:
  6. Blow-up ; Existence and non-existence results ; Semilinear laplacian problems ; Singular problem
  7. Source: European Journal of Mathematics ; Volume 3, Issue 1 , 2017 , Pages 150-170 ; 2199675X (ISSN)
  8. URL: https://link.springer.com/article/10.1007/s40879-017-0129-5