منابع مشابه
STABLE AND SINGULAR SOLUTIONS OF THE EQUATION ∆u = 1 u
We study properties of the semilinear elliptic equation ∆u = 1 u on domains in R, with an eye toward nonnegative singular solutions as limits of positive smooth solutions. We prove the nonexistence of such solutions in low dimensions when we also require them to be stable for the corresponding variational problem. The problem of finding singular solutions is related to the general study of sing...
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The symmetry reduction of the equation u 0 +∇ u − 4 5 ∇u = 0 to ordinary differential equations with respect to all subalgebras of rank three of the algebra A E (1) ⊕ AC (3) is carried out. New invariant solutions are constructed for this equation.
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The steady-state form of the Klein-Gordon equation is given by (•) Au = u-u3, u = u(X), X&R3. 3 For solutions which are spherically symmetric, (*) takes the form ü + lujr = u — u , 3 u = u(r), where r is the distance from the origin in R . The function y = ru satisfies (* *) j' = y y ¡r . It is known that (•*) has solutions {yn}n=Q, where yn has exactly n zeros in (0, °°), and where y(0) = y(°°...
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Valdis Laan in [5] introduced an extension of strong flatness which is called weak pullback flatness. In this paper we introduce a new property of acts over monoids, called U-WPF which is an extension of weak pullback flatness and give a classification of monoids by this property of their acts and also a classification of monoids when this property of acts implies others. We also show that regu...
متن کاملPositive Solutions of the Equation U + U P = 0 on a Bounded Domain
These are are the notes of a series of lectures given in the seminar "Topics in Nonlinear Analysis" at the "Center for Nonlinear Partial Diierential Equations (Delft-Leiden)", in autumn of 1991. In these course notes we present the basic theorems, and the necessary background as a selfcontained resum e on the problem (P) n u + u p = 0 in ; u = 0 on @: We restrict ourselves mainly to the subcrit...
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ژورنال
عنوان ژورنال: Nature
سال: 1902
ISSN: 0028-0836,1476-4687
DOI: 10.1038/065247a0