Positive solution for Hénon type equations with critical Sobolev growth
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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.
CitationTakahashi, K. (2018). Positive solution for Hénon type equations with critical Sobolev growth. Electronic Journal of Differential Equations, 2018(194), pp. 1-17.
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