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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Nonexistence of nodal solutions of elliptic equations with critical growth in $\mathbb {R}^2$


Authors: Adimurthi and S. L. Yadava
Journal: Trans. Amer. Math. Soc. 332 (1992), 449-458
MSC: Primary 35J65; Secondary 35B05
DOI: https://doi.org/10.1090/S0002-9947-1992-1050083-3
MathSciNet review: 1050083
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Abstract: Let $f(t) = h(t){e^{b{t^2}}}$ be a function of critical growth. Under a suitable assumption on $h$, we prove that \[ \begin {array}{*{20}{c}} { - \Delta u = f(u)} \hfill & {{\text {in}}\;B(R) \subset {\mathbb {R}^2},} \hfill \\ {u = 0} \hfill & {{\text {on}}\;\partial B(R),} \hfill \\ \end {array} \] does not admit a radial solution which changes sign for sufficiently small $R$.


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Article copyright: © Copyright 1992 American Mathematical Society