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Principal eigenvalues for indefinite weight problems in all of

Authors:	N Bejhaj Rhouma

Institution:	Institut Préparatoire aux Études d'Ingénieurs de Tunis, 2, rue Jawaherlel Nehru, 1008 Montfleury, Tunis, Tunisia

Abstract:	We show the existence of principal eigenvalues of the problem $-\triangle u=\lambda gu$ in $\mathbb{R}^{d}$ where is an indefinite weight function. The existence of a continuous family of principal eigenvalues is demonstrated. Also, we prove the existence of a principal eigenvalue for which the principal eigenfunction $u\rightarrow 0$ at $\infty$ .

Keywords:	Indefinite weight eigenvalue Kato-class Green function

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