Existence and multiplicity results for a semilinear elliptic eigenvalue problem
Philippe Clément, Guido Sweers (1987)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Philippe Clément, Guido Sweers (1987)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Jacqueline Fleckinger, Jesús Hernández, François De Thélin (2003)
RACSAM
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We study the existence of principal eigenvalues for differential operators of second order which are not necessarily in divergence form. We obtain results concerning multiplicity of principal eigenvalues in both the variational and the general case. Our approach uses systematically the Krein-Rutman theorem and fixed point arguments for the inverse of the spectral radius of some associated problems. We also use a variational characterization for both the self-adjoint and the general case. ...
Takashi Suzuki (1992)
Annales de l'I.H.P. Analyse non linéaire
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Isabeau Birindelli, Françoise Demengel (2004)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Robert Dalmasso (1995)
Revista Matemática Iberoamericana
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In this paper we discuss the uniqueness of positive solutions of the nonlinear second order system -u'' = g(v), -v'' = f(u) in (-R,R), u(±R) = v(±R) = 0 where f and g satisfy some appropriate conditions. Our result applies, in particular, to g(v) = v, f(u) = u, p > 1, or f(u) = λu + au + ... + au, with p > 1, a > 0 for j = 1, ..., k and 0 ≤ λ < μ where μ = π/4R.
Luigi Orsina (1993)
Rendiconti del Seminario Matematico della Università di Padova
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Karim Chaïb (2002)
Publicacions Matemàtiques
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The purpose of this paper is to extend the Díaz-Saá’s inequality for the unbounded domains as RN. The proof is based on the Picone’s identity which is very useful in problems involving p-Laplacian. In a second part, we study some properties of the first eigenvalue for a system of p-Laplacian. We use Díaz-Saá’s inequality to prove uniqueness and Egorov’s theorem for the isolation. These results generalize J. Fleckinger, R. F. Manásevich, N. M. Stavrakakis...