Displaying similar documents to “The Lane-Emden Function and Nonlinear Eigenvalues Problems”

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.

Short-time heat flow and functions of bounded variation in R N

Michele Miranda, Diego Pallara, Fabio Paronetto, Marc Preunkert (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

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We prove a characterisation of sets with finite perimeter and B V functions in terms of the short time behaviour of the heat semigroup in R N . For sets with smooth boundary a more precise result is shown.

Classification of initial data for the Riccati equation

N. Chernyavskaya, L. Shuster (2002)

Bollettino dell'Unione Matematica Italiana

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We consider a Cauchy problem y ′ ⁢ x + y 2 ⁢ x = q ⁢ x , y ⁢ x x = x 0 = y 0 where x 0 , y 0 ∈ R and q ⁢ x ∈ L 1 loc ⁢ R is a non-negative function satisfying the condition: ∫ - ∞ x q ⁢ t ⁢ d ⁢ t > 0 , ∫ x ∞ q ⁢ t ⁢ d ⁢ t > 0 ⁢  for  ⁢ x ∈ R . We obtain the conditions under which y ⁢ x can be continued to all of R . This depends on x 0 , y 0 and the properties of q ⁢ x .