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On the Fredholm Alternative for the -Laplacian

Authors:	Paul A Binding Pavel Drá bek Yin Xi Huang

Institution:	Department of Mathematics & Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4 Pavel Drábek ; 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:	Consider $\begin{equation}\left \{\begin{split} &-(\|u'\|^{p-2}u')'=\lambda \|u\|^{p-2}u+f(x), x\in (0, 1), &u(0)=\beta u'(0), \quad u'(1)=0,\end{split}\right . \end{equation}$ where and $\beta \in \mathbb{R}\cup \{\infty \}$ and let $\lambda _{1}$ be the principal eigenvalue of the problem with $f(x)\equiv 0$ . For $\lambda =\lambda _{1}$ , we discuss for which values of and $\beta$ the Fredholm alternative holds.

Keywords:	Fredholm alternative the $p$-Laplacian

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