Spectrum of one dimensional p-Laplacian operator with indefinite weight

By M. Moussa, A. Anane, O. Chakrone. 2002

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This paper is concerned with the nonlinear boundary eigenvalue problem (ju 0 j p 2 u 0 ) 0 = m juj p 2 u u 2 I =]a; b[; u(a) = u(b) = 0; where p > 1, is a real parameter, m is an indenite weight, and a, b are real numbers. We prove there exists a unique sequence of eigenvalues for this problem. Each eigenvalue is simple and veries the strict monotonicity property with respect to the weight m and the domain I, the k-th eigenfunction, corresponding to the k-th eigenvalue, has exactly k 1 zeros in (a; b). At the end, we give a simple variational formulation of eigenvalues.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

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