New solutions of equations on n
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 30 (2001) no. 3-4, pp. 535-563.
@article{ASNSP_2001_4_30_3-4_535_0,
     author = {Dancer, Edward Norman},
     title = {New solutions of equations on $\mathbb {R}^n$},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {535--563},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 30},
     number = {3-4},
     year = {2001},
     mrnumber = {1896077},
     zbl = {1025.35009},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2001_4_30_3-4_535_0/}
}
TY  - JOUR
AU  - Dancer, Edward Norman
TI  - New solutions of equations on $\mathbb {R}^n$
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 2001
SP  - 535
EP  - 563
VL  - 30
IS  - 3-4
PB  - Scuola normale superiore
UR  - http://www.numdam.org/item/ASNSP_2001_4_30_3-4_535_0/
LA  - en
ID  - ASNSP_2001_4_30_3-4_535_0
ER  - 
%0 Journal Article
%A Dancer, Edward Norman
%T New solutions of equations on $\mathbb {R}^n$
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 2001
%P 535-563
%V 30
%N 3-4
%I Scuola normale superiore
%U http://www.numdam.org/item/ASNSP_2001_4_30_3-4_535_0/
%G en
%F ASNSP_2001_4_30_3-4_535_0
Dancer, Edward Norman. New solutions of equations on $\mathbb {R}^n$. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 30 (2001) no. 3-4, pp. 535-563. http://www.numdam.org/item/ASNSP_2001_4_30_3-4_535_0/

[1] A. Ambrosetti - C. Coti-Zelati - I. Ekeland, Symmetry breaking in Hamiltonian systems, Differential Equations 67 (1987), 165-184. | MR | Zbl

[2] A. Ambrosetti - Garcia Azorero - I. Peral, Perturbations of Δu + un+2)/(n-2) = 0, the scalar curvature problem on Rn and related topics, J. Funct. Anal. 165 (1999), 117-149. | Zbl

[3] B. Buffoni - E.N. Dancer - J. Toland, The regularity and local bifurcation of Stokes waves, Arch. Rational Mech. Anal. 152 (2000), 207-240. | MR | Zbl

[4] B. Buffoni - E.N. Dancer - J. Toland, The subharmonic bifurcation of Stokes waves, Arch. Rational Mech. Anal. 152 (2000), 241-271. | MR | Zbl

[5] H. Cartan, "Calcul differentiel, Hermann, Paris, 1967. | MR | Zbl

[6] M. Crandall - P. Rabinowitz, Bifurcation from simple eigenvalues, J. Funct. Anal. 8 (1971), 321-340. | MR | Zbl

[7] M. Crandall - P. Rabonowitz, Bifurcation perturbation of simple eigenvalues and linearized stability, Arch. Rational Mech. Anal. 52 (1973), 161-180. | MR | Zbl

[8] E.N. Dancer, On the uniqueness of the positive solution of a singularly perturbed problem, Rocky Mountain J. Math. 25 (1995), 957-975. | MR | Zbl

[9] E.N. Dancer, On positive solutions of some singularly perturbed problems where the nonlinearity changes sign, Top. Methods Nonlinear Anal. 5 (1995), 141-175. | MR | Zbl

[10] E.N. Dancer, "Weakly nonlinear equations on long or thin domains", Mem. Amer. Math. Soc. 501 Providence, RI, 1993. | MR | Zbl

[11] E.N. Dancer, On the structure of solutions of nonlinear eigenvalue problems, Indiana Univ. Math. J. 23 (1974), 1069-1076. | MR | Zbl

[12] E.N. Dancer, Global structure of the solution set of non-linear real analytic eigenvalue problems, Proc. London Math. Soc. 26 (1973), 359-384.

[13] E.N. Dancer, Infinitely many turning points for some supercritical problems, to appear in Annali di Matematica. | MR | Zbl

[14] E.N. Dancer, The G-invariant implicit function theorem in infinite dimensions, Proc. Royal Soc. Edinburgh 92A (1982), 13-30. | MR | Zbl

[15] E.N. Dancer, The G-invariant implicit function theorem in infinite dimensions II, Proc. Royal Soc Edinburgh 102A (1986), 211-220. | MR | Zbl

[16] E.N. Dancer, Some notes on the method of moving planes, Bull Austra. Math. Soc. 46 (1992), 425-434. | MR | Zbl

[17] B. Gidas, Symmetry properties and isolated singularities of positive solutions of nonlinear elliptic equations, pp. 255-273 In: "Nonlinear partial differential equations in science and engineering", R. Sternberg (ed.), Marcel Dekker, New York, 1980. | MR | Zbl

[18] B. Gidas, W.M. Ni - L. Nirenberg, Symmetry of positive solutions of nonlinear elliptic equations on Rn, pp. 369-402 In: "Mathematical Analysis and Applications", Part A, L. Nachbin (ed.), Academic Press, New York, 1981. | Zbl

[19] D. Gilbarg - N. Trudinger, "Elliptic partial differential equations of second order", 2nd edition, Springer-Verlag, Berlin, 1983. | MR | Zbl

[20] W. Hayman - P. Kennedy, "Subharmonic functions", Academic Press, London, 1976. | Zbl

[21] R. Hewitt - K. Stromberg, "Real and abstract analysis", Springer-Verlag, Berlin, 1965. | Zbl

[22] C. Isnard, The topological degree on Banach manifolds, pp. 291-314 In: "Global analysis and its applications", Vol II, International atomic energy agency, Vienna, 1974. | MR | Zbl

[23] T. Kato, "Perturbation theory for linear operators", Springer-Verlag, Berlin, 1966. | MR | Zbl

[24] O. Kavian, "Introduction à la théorie des points critiques", Springer-Verlag, Berlin, 1993. | MR

[25] H. Kielhofer, A bifurcation theorem for potential operators, J. Funct. Anal. 77 (1988), 1-8. | MR | Zbl

[26] M.A. Kransnosel'Skii, "Topological methods in the theory of nonlinear integral equations", Perganon, New York, 1964.

[27] M.K. Kwong - Liqun Zhang, Uniqueness of the positive solution of Δu + f(u) = 0, in an annulus, Differential Integral Equations 4 (1991), 583-599. | Zbl

[28] O. Ladyzhenskaya - N. Uraltseva, "Linear and quasilinear elliptic equations", Academic Press, New York, 1968. | MR | Zbl

[29] P. Rabinowitz, A bifurcation theorem for potential operators, J. Funct. Anal. 25 (1977), 412-424. | MR | Zbl

[30] M. Reed - B. Simon, "Methods of modem mathematical physics volume IV: analysis of operators ", Academic Press, New York, 1978. | MR | Zbl

[31] O. Rey, The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent, J. Funct. Anal. 89 (1990), 1-52. | MR | Zbl

[32] K. Rybakowski, "The homotopy index and partial differential equations", Springer-Verlag, Berlin, 1987. | MR | Zbl

[33] J. Saut - R. Temam, Generic properties of nonlinear boundary value problems, Comm. Partial Differential Equations 4 (1979), 293-319. | MR | Zbl

[34] J. Toland, On positive solutions of -Δu = F(x, u), Math Z. 182 (1983), 351-357. | Zbl

[35] M.M. Vainberg, "Variational methods for the study of nonlinear operators", Holden Day, San Francisco, 1964. | MR | Zbl

[36] L. Ward, "Topology", Marcel Dekker, New York, 1972. | MR | Zbl

[37] H. Zou, Slow decay and the Harnack inequality for positive solutions of Δu + up = 0 in Rn, Differential Integral Equations 8 (1995), 1355-1368. | Zbl