Zhang, QiHuang, Jianping2022-09-192022-09-192017-11-27Zhang, Q., & Huang, J. (2017). Positive solutions for p-Laplacian equations of Kirchhoff type problem with a parameter. <i>Electronic Journal of Differential Equations, 2017</i>(292), pp. 1-11.1072-6691https://hdl.handle.net/10877/16153In 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.Text11 pages1 file (.pdf)enAttribution 4.0 InternationalPositive solutionp-Laplacian equationIterative techniqueArticle