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  1. Existence of positive solution for nonlocal singular fourth order Kirchhoff equation with Hardy potential
Existence of positive solution for nonlocal singular fourth order Kirchhoff equation with Hardy potential
387 viewed

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

Ansari, H

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

Ansari, H ; Sharif University of Technology

387 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