Article
Keywords:
elliptic equations; radial solutions; critical Sobolev exponent
Summary:
In this paper we construct radial solutions of equation (1) (and (13)) having prescribed number of nodes.
References:
[1] Adimurthi:
Existence of positive solutions of the semilinear Dirichlet problem with critical growth for the $n$-Laplacian. Ann. Scuola Norm. Sup. Pisa 12.1 (1990), 393-413.
MR 1079983 |
Zbl 0732.35028
[2] Ambrosetti A., Rabinowitz P.H.:
Dual variational methods in critical point theory and applications. J. Funct. Anal. 14 (1973), 349-381.
MR 0370183 |
Zbl 0273.49063
[3] Bartsch Th., Willem M.:
Infinitely many radial solutions of a semilinear elliptic problem on $\Bbb R^N$. Arch. Rat. Mech. Anal. 124 (1993), 261-274.
MR 1237913
[4] Bianchi G., Chabrowski J., Szulkin A.:
On symmetric solutions of an elliptic equation involving critical Sobolev exponent. Nonlinear Analysis, TMA 25(1) (1995), 41-59.
MR 1331987
[5] Ladyzhenskaya O.A., Ural'ceva O.A.:
Linear and Quasilinear Elliptic Equations. Academic Press New York (1968).
MR 0244627
[6] Lions P.L.:
Symétrie et compacité dans les espaces de Sobolev. J. Funct. Anal. 49 (1982), 315-334.
MR 0683027 |
Zbl 0501.46032
[7] Yi Li, Wei-Ming Ni:
On the asymptotic behavior and radial symmetry of positive solutions of semilinear elliptic equations in $\Bbb R^n$, I Asymptotic behavior, II Radial symmetry. Arch. Rat. Mech. Anal. 118 (1992), 195-222, 223-243.
MR 1158935
[8] Rother W.:
Some existence results for the equation $\Delta U+K(x)U^p=0$. Commun. in P.D.E. 15.10 (1990), 1461-1473.
MR 1077474
[9] Stuart C.A.:
Bifurcation in $L^p(\Bbb R^N)$ for a semilinear elliptic equations. Proc. London Math. Soc. 57(3) (1988), 511-541.
MR 0960098 |
Zbl 0673.35005
[10] Talenti G.:
Best constants in Sobolev inequality. Ann. Mat. Pura Appl. 110 (1976), 353-372.
MR 0463908
[11] Vainberg M.M.:
Variational Method and Method of Monotone Operators in the Theory of Nonlinear Equations. John Wiley & Sons New York-Toronto (1973).
MR 0467428 |
Zbl 0279.47022