On a conjecture of Lin-Ni for a semilinear Neumann problem

Adimurthi; Yadava, S. L.

doi:10.1090/S0002-9947-1993-1156299-0

On a conjecture of Lin-Ni for a semilinear Neumann problem

Authors: Adimurthi and S. L. Yadava
Journal: Trans. Amer. Math. Soc. 336 (1993), 631-637
MSC: Primary 35J65; Secondary 35P30
DOI: https://doi.org/10.1090/S0002-9947-1993-1156299-0
MathSciNet review: 1156299
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Abstract: Let $\Omega$ be a bounded domain in ${\mathbb{R}^n}$ $(n \geq 3)$ and $\lambda > 0$ . We consider

$\begin{displaymath}\begin{array}{*{20}{c}} { - \Delta u + \lambda u = {u^{(n + 2... ... }} = 0} & {{\text{on}}} \; {\partial \Omega ,} \\ \end{array} \end{displaymath}$

and show that for $\lambda$ sufficiently small, the minimal energy solutions are only constants.

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