Positive solutions for p-Laplacian equations of Kirchhoff type problem with a parameter
MetadataShow full metadata
In this article, we consider the existence and non-existence of positive solutions for the Kirchhoff type equation
-(α + λM (∫Ω |∇u|pdx)) ∆pu = ƒ(u), in Ω,
u = 0, on ∂Ω,
where Ω ⊂ ℝN is a bounded domain with a smooth boundary ∂Ω, α is a positive constant, N ≥ 3, λ ≥ 0, 2 ≤ p < N, M and ƒ, we show that the above problem has at least one positive solution when λ is small and has no nonzero solution when λ is large. Our argument is based on iterative technique and variational methods.
CitationZhang, Q., & Huang, J. (2017). Positive solutions for p-Laplacian equations of Kirchhoff type problem with a parameter. Electronic Journal of Differential Equations, 2017(292), pp. 1-11.
This work is licensed under a Creative Commons Attribution 4.0 International License.