Positive solutions for p-Laplacian equations of Kirchhoff type problem with a parameter
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Date
2017-11-27
Authors
Zhang, Qi
Huang, Jianping
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
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.
Description
Keywords
Positive solution, p-Laplacian equation, Iterative technique
Citation
Zhang, 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.
Rights
Attribution 4.0 International