Displaying similar documents to “The effect of variational framework on the spectral asymptotics for nonlinear elliptic two-parameter problems”

The Lane-Emden Function and Nonlinear Eigenvalues Problems

Ould Ahmed Izid Bih Isselkou (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

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We consider a semilinear elliptic eigenvalues problem on a ball of ℜ n and show that all the eigenfunctions and eigenvalues, can be obtained from the Lane-Emden function.

Strong asymptotic stability for n-dimensional thermoelasticity systems

Mohammed Aassila (1998)

Colloquium Mathematicae

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We use a new approach to prove the strong asymptotic stability for n-dimensional thermoelasticity systems. Unlike the earlier works, our method can be applied in the case of feedbacks with no growth assumption at the origin, and when LaSalle's invariance principle cannot be applied due to the lack of compactness.

Ferromagnetic integrals, correlations and maximum principles

Johannes Sjöstrand (1994)

Annales de l'institut Fourier

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For correlations of the form (0.2) we consider a critical case and prove power decay upper bounds in terms of the fundamental solution of a certain elliptic operator. This is achieved by improving the use of a maximum principle. We also formulate a general maximum principle and give two applications.

Universal solutions of a nonlinear heat equation on ℝ N

Thierry Cazenave, Flávio Dickstein, Fred B. Weissler (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In this paper, we study the relationship between the long time behavior of a solution u ( t , x ) of the nonlinear heat equation u t - Δ u + | u | α u = 0 on ℝ N (where α > 0 ) and the asymptotic behavior as | x | → ∞ of its initial value u 0 . In particular, we show that if the sequence of dilations λ n 2 / α u 0 ( λ n · ) converges weakly to z ( · ) as λ n → ∞ , then the rescaled solution t 1 / α u ( t , · t ) converges uniformly on ℝ N to 𝒰 ( 1 ) z along the subsequence t n = λ n 2 , where 𝒰 ( t ) is an appropriate flow. Moreover, we show there exists an initial value U 0 such that the set of all possible z attainable...