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### On the closed solution to some nonhomogeneous eigenvalue problems with p-Laplacian

 Citace: [] DRÁBEK, P., MANÁSEVICH, R. On the closed solution to some nonhomogeneous eigenvalue problems with p-Laplacian. Differential and Integral Equations, 1999, roč. 12, č. 6, s. 773-788. ČLÁNEK eng On the closed solution to some nonhomogeneous eigenvalue problems with p-Laplacian 1999 Pavel Drábek , Raul Manásevich We deal with the Dirichlet, Neumann and periodic eigenvalue problems for the equation (|u'|^{p-2} u')'+\lambda|u|^{q-2}u =0, on (0,T), where T>0, \lambda >0, and p,q>1. For those problems we obtain a complete description of the spectra and a closed form representation of the corresponding eigenfunctions. As an application of our results we present sharp Poincaré and Wirtinger inequalities for imbeddings W^{1,p}_0 (0,T) into L^q (0,T) and W^{1,p}_T (0,T) into L^q(0,T), respectively.

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