M. F. Barnsley (auth.), C. Bardos, J. M. Lasry, M. Schatzman's Bifurcation and Nonlinear Eigenvalue Problems: Proceedings, PDF

By M. F. Barnsley (auth.), C. Bardos, J. M. Lasry, M. Schatzman (eds.)

ISBN-10: 3540097589

ISBN-13: 9783540097587

ISBN-10: 3540386378

ISBN-13: 9783540386377

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Extra info for Bifurcation and Nonlinear Eigenvalue Problems: Proceedings, Université de Paris XIII, Villetaneuse, France, October 2–4, 1978

Sample text

The existence cf such a "minimal radius" R o is from the phy- sical view point an interesting phenomena, which is related to a form of the Heisenberg uncertainty principle (see [18] for the precise formulation). 39 BIBLIOGRAPHY ill S. Agmon, A. Douglis and L. Nirenberg : Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions; Comm. Pure and Applied Math. 12 (1959) p. 623-727 Part. I. [2] A. H. Rabinowitz : Dual variational methods in critical point theory and applications) J.

E. in ~n we have uR(O) = max u R u(O) = lira URn(O) >- ~ , BR is positive. u L = lira ~ u(x), as O~u -< B we have L ~ [0,~] . Ix Jr+. Furthermore as ~R' ~BR UR'(~R')

Such f(x,u) ~ ku , and if Av + tKv = tf(x,u) (]8), for some + tKu t ~[0,]] u - < F u = v, we have in . 2. on $~ . ]. will be given in section IV. w 32 IV. ]. ]. = ~ lu p - ~u q - m~ We have BR heorem classical equations (see state the result we be positive cons- : Under result , radial, decreasing (where (2) is a necessary results case. in r = [xl) : ~n to solve ~u q - mu > O. 2. l, ~ , m u @ C°°(~ n) for solving (of radius R) with Dirichlet the following ~ that of (I). More general R -~+ ~ . We - 0~ (I) in here is a kind of model but in a ball (I-R) We first m >O] D ~ u ( x ) ~ C e $ ~ m In this section we consider letting solution In [5] , we prove solution considered (|) we in non linear Schr~dinger o~ , let ~q+l q+l ~ (u(x) trivial of equation wares or non linear .

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Bifurcation and Nonlinear Eigenvalue Problems: Proceedings, Université de Paris XIII, Villetaneuse, France, October 2–4, 1978 by M. F. Barnsley (auth.), C. Bardos, J. M. Lasry, M. Schatzman (eds.)


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