Displaying similar documents to “The construction of principal spectral curves for Lane-Emden systems and applications”

On the existence of multiple principal eigenvalues for some indefinite linear eigenvalue problems.

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. ...

Uniqueness of positive solutions of nonlinear second order systems.

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.

Extension of Díaz-Saá's inequality in R and application to a system of p-Laplacian.

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...