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Bifurcation problems for the
Authors:Pavel Drá  bek   Yin Xi Huang
Affiliation:Department of Mathematics, University of West Bohemia, P.O. Box 314, 30614 Pilsen, Czech Republic

Yin Xi Huang ; Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee 38152

Abstract:In this paper we consider the bifurcation problem

begin{equation*}-text {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*}-text {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.

Keywords:$p$-Laplacian   global positive solutions   weighted spaces
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