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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Existence and nonexistence of positive eigenfunctions for the $p$-Laplacian
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by P. A. Binding and Y. X. Huang PDF
Proc. Amer. Math. Soc. 123 (1995), 1833-1838 Request permission

Abstract:

We study the relation between (i) the principal eigencurve, i.e., the graph of ${\mu _1}$ satisfying \begin{equation}\tag {$ \ast $} - {\operatorname {div}}(|\nabla u{|^{p - 2}}\nabla u) + (q(x) - \lambda w(x))|u{|^{p - 2}}u = {\mu _1}(\lambda )|u{|^{p - 2}}\mu \end{equation} on a smooth bounded domain $\Omega$ in ${{\mathbf {R}}^N}$ with $p > 1$, and (ii) existence and nonexistence of positive solutions of $( \ast )$ with ${\mu _1}(\lambda ) = 0$. Eigencurve arguments are used extensively.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 1833-1838
  • MSC: Primary 35P30; Secondary 47H12, 47N20
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1260160-8
  • MathSciNet review: 1260160