Loading...

Existence of positive solution for nonlocal singular fourth order Kirchhoff equation with Hardy potential

Ansari, H ; Sharif University of Technology

234 Viewed
  1. Type of Document: Article
  2. DOI: 10.1007/s11117-017-0484-y
  3. Abstract:
  4. This paper is concerned with the existence of positive solution to a class of singular fourth order elliptic equation of Kirchhoff type (Formula Presented.)▵2u-λM(‖∇u‖2)▵u-μ|x|4u=h(x)uγ+k(x)uα,under Navier boundary conditions, u= ▵u= 0. Here Ω⊂ RN, N≥ 1 is a bounded C4-domain, 0 ∈ Ω, h(x) and k(x) are positive continuous functions, γ∈ (0 , 1) , α∈ (0 , 1) and M: R+→ R+ is a continuous function. By using Galerkin method and sharp angle lemma, we will show that this problem has a positive solution for m0 and 0 < μ< μ∗. Here μ∗=(N(N-4)4)2 is the best constant in the Hardy inequality. Besides, if μ= 0 , λ> 0 and h, k are Lipschitz functions, we show that this problem has a positive smooth solution. If h,k∈C2,θ0(Ω¯) for some θ0∈ (0 , 1) , then this problem has a positive classical solution. © 2017, Springer International Publishing
  5. Keywords:
  6. Galerkin method ; Hardy potential ; Nonlinear kirchhoff equation ; Sharp angle lemma ; Singular elliptic equation
  7. Source: Positivity ; Volume 21, Issue 4 , 2017 , Pages 1545-1562 ; 13851292 (ISSN)
  8. URL: https://link.springer.com/article/10.1007/s11117-017-0484-y