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Transactions of the American Mathematical Society

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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{displaymath}\begin{array}{*{20}{c}} { - \Delta u = f(u)} \hfill & {{\text... ...} \hfill & {{\text{on}}\;\partial B(R),} \hfill \\ \end{array} \end{displaymath}

does not admit a radial solution which changes sign for sufficiently small $ R$.

References [Enhancements On Off] (What's this?)

  • [1] Adimurthi and S. L. Yadava, Multiplicity results for semilinear elliptic equations in a bounded domain of $ {\mathbb{R}^2}$ involving critical exponents, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 27 (1990), 481-504. MR 1093706 (92c:35045)
  • [2] F. V. Atkinson and L. A. Peletier, Ground states and Dirichlet problem for $ - \Delta u = f(u)$ in $ {\mathbb{R}^2}$, Arch. Rational Mech. Anal. 96 (1986), 147-165. MR 853971 (87k:35080)
  • [3] -, Emden-Fowler equations involving critical exponents, Nonlinear Anal. TMA 10 (1986), 755-776. MR 851145 (87j:34039)
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  • [5] G. Cerami, S. Solomini and M. Struwe, Some existence results for super linear elliptic boundary value problems involving critical exponents, J. Functional Anal. 69 (1986), 289-306. MR 867663 (88b:35074)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1992-1050083-3
Article copyright: © Copyright 1992 American Mathematical Society

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