Positive solution for Hénon type equations with critical Sobolev growth
Date
2018-11-28
Authors
Takahashi, Kazune
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We investigate the Hénon type equation involving the critical Sobolev exponent with Dirichret boundary condition
-∆u = λΨu + |x|α u2*-1
in Ω included in a unit ball, under several conditions. Here, Ψ is a non-trivial given function with 0 ≤ Ψ ≤ 1 which may vanish on ∂Ω. Let λ1 be the first eigenvalue of the Dirichret eigenvalue problem -∆φ = λΨφ in Ω. We show that if the dimension N ≥ 4 and 0 < λ < λ1, there exists a positive solution for small α > 0. Our methods include the mountain pass theorem and the Talenti function.
Description
Keywords
Critical Sobolev exponent, Henon equation, Mountain Pass Theorem, Talenti function
Citation
Takahashi, K. (2018). Positive solution for Hénon type equations with critical Sobolev growth. <i>Electronic Journal of Differential Equations, 2018</i>(194), pp. 1-17.
Rights
Attribution 4.0 International