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### A bifurcation problem for the principal eigencurve of the p-Laplacian

 Citace: [] DRÁBEK, P., ELKHALIL, A., TOUZANI, A. A bifurcation problem for the principal eigencurve of the p-Laplacian. Applicable Analysis, 1999, roč. 72, č. 3-4, s. 399-410. ISSN: 0003-6811 ČLÁNEK eng A bifurcation problem for the principal eigencurve of the p-Laplacian 1999 Pavel Drábek , A. Elkhalil , Abdelfettah Touzani We study the following bifurcation problem in any bounded domain \Omega in \R^N -\Delta_pu -\lambda m(x)|u|^{p-2}u=\mu|u|^{p-2}u+f(x,u,\lambda,\mu),u\inW^{1,p}_0(\Omega). We prove that for any \lambda \in \R, the principal eigenvalue \mu_1(\lambda) of te eigenvalue problem: -\Delta_pu - \lambda m(x)|u|^{p-2} u=\mu|u|^{p-2} u in \Omega, u\in W^{1,p}_0 (\Omega), is a bifurcation point of the problem mentioned above.

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