Linear mathematics in infinite dimensions: signals, BVPs, by Gerlach U.H.

By Gerlach U.H.

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Bari (2001). : New solutions of equations on Rn . Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 30, no. 3-4, 535–563 (2001). : Local mountain passes for semilinear elliptic problems in unbounded domains. Calc. Var. 4, 121-137 (1996). : Semi-classcal states for nonlinear Schr¨ odinger equations. J. Funct. Anal. 149, 245-265 (1997). [15] Floer, A. , Weinstein, A. : Nonspreading wave packets for the cubic Schr¨ odinger equation with a bounded potential. J. Funct. Anal. : Symmetry of positive solutions of nonlinear elliptic equations in Rn .

2, requires a more delicate analysis. In particular, wee suspect that concentration occurs in general along sequences εj → 0 as in [23]. Acknowledgments A. A. and A. M. are supported by MURST, under the project Variational Methods and Nonlinear Differential Equations. N. is partially supported by the National Science Foundation. The authors wish to thank some institutions for the hospitality and support. A. M. A. : Homoclinics: Poincar´e-Melnikov type results via a variational approach. Ann. Inst.

When p > n−2 it is sufficient to consider a cutoff function FK as in Section 5. The above proof yields bifurcation of non-radial solutions of Iε,K = 0. The L∞ bounds on the radial solutions and standard regularity results imply that non-radial solutions which are sufficiently close to the radial ones (in H 1 (Rn )) are also uniformly bounded. Hence these critical points are also solutions of (15). 6 Bifurcation of non symmetric solutions of some classes of elliptic equations on R n has been recently studied in [12, 30].

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