Bifurcation problems for the $p$-Laplacian in $R^n$
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- by Pavel Drábek and Yin Xi Huang PDF
- Trans. Amer. Math. Soc. 349 (1997), 171-188 Request permission
Abstract:
In this paper we consider the bifurcation problem \begin{equation*} -\operatorname {div} (|\nabla u|^{p-2}\nabla u)=\lambda g(x)|u|^{p-2}u+f(\lambda , x, u), \end{equation*} in $R^N$ with $p>1$. We show that a continuum of positive solutions bifurcates out from the principal eigenvalue $\lambda _{1}$ of the problem \begin{equation*}-\operatorname {div} (|\nabla u|^{p-2}\nabla u)=\lambda g(x)|u|^{p-2}u. \end{equation*} Here both functions $f$ and $g$ may change sign.References
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Additional Information
- Pavel Drábek
- Affiliation: Department of Mathematics, University of West Bohemia, P.O. Box 314, 30614 Pilsen, Czech Republic
- Yin Xi Huang
- Affiliation: Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee 38152
- Email: huangy@mathsci.msci.memphis.edu
- Received by editor(s): November 18, 1994
- Received by editor(s) in revised form: March 10, 1995
- Additional Notes: The first author was partially supported by the Grant Agency of the Czech Republic under the Grant No. 201/94/0008
- © Copyright 1997 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 349 (1997), 171-188
- MSC (1991): Primary 35B32, 35J70, 35P30
- DOI: https://doi.org/10.1090/S0002-9947-97-01788-1
- MathSciNet review: 1390979