On the Uniqueness of the Second Bound State Solution of a Semilinear Equation
Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 6, p. 2091-2110
@article{AIHPC_2009__26_6_2091_0,
author = {Cort\'aZar, Carmen and Garc\'\i A-Huidobro, Marta and Yarur, Cecilia S.},
title = {On the Uniqueness of the Second Bound State Solution of a Semilinear Equation},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {26},
number = {6},
year = {2009},
pages = {2091-2110},
doi = {10.1016/j.anihpc.2009.01.004},
zbl = {pre05649865},
mrnumber = {2569887},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2009__26_6_2091_0}
}

CortáZar, Carmen; GarcíA-Huidobro, Marta; Yarur, Cecilia S. On the Uniqueness of the Second Bound State Solution of a Semilinear Equation. Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 6, pp. 2091-2110. doi : 10.1016/j.anihpc.2009.01.004. http://www.numdam.org/item/AIHPC_2009__26_6_2091_0/

[1] Berestycki H., Lions P. L., Non Linear Scalar Fields Equations I. Existence of a Ground State, Arch. Ration. Mech. Anal. 82 (1983) 313-345. | MR 695535 | Zbl 0533.35029

[2] Caristi G., Mitidieri E., Nonexistence of Positive Solutions of Quasilinear Equations, Adv. Differential Equations 2 (3) (1997) 319-359. | MR 1441847 | Zbl 1023.34500

[3] Chen C. C., Lin C. S., Uniqueness of the Ground State Solutions of $\Delta u+f\left(u\right)=0$ in ${R}^{N}$, $N\ge 3$, Comm. Partial Differential Equations 16 (1991) 1549-1572. | MR 1132797 | Zbl 0753.35034

[4] Coffman C. V., Uniqueness of the Ground State Solution of $\Delta u-u+{u}^{3}=0$ and a Variational Characterization of Other Solutions, Arch. Ration. Mech. Anal. 46 (1972) 81-95. | MR 333489 | Zbl 0249.35029

[5] Coffman C. V., A Nonlinear Boundary Value Problem With Many Positive Solutions, J. Differential Equations 54 (1984) 429-437. | MR 760381 | Zbl 0569.35033

[6] Cortázar C., Felmer P., Elgueta M., On a Semilinear Elliptic Problem in ${R}^{N}$ With a Non Lipschitzian Nonlinearity, Adv. Differential Equations 1 (1996) 199-218. | MR 1364001 | Zbl 0845.35031

[7] Cortázar C., Felmer P., Elgueta M., Uniqueness of Positive Solutions of $\Delta u+f\left(u\right)=0$ in ${R}^{N}$, $N\ge 3$, Arch. Ration. Mech. Anal. 142 (1998) 127-141. | MR 1629650 | Zbl 0912.35059

[8] Cortázar C., García-Huidobro M., On the Uniqueness of Ground State Solutions of a Semilinear Equation Containing a Weighted Laplacian, Comm. Pure. Appl. Anal. 5 (2006) 813-826. | MR 2246009 | Zbl 1137.35029

[9] Erbe L., Tang M., Uniqueness Theorems for Positive Solutions of Quasilinear Elliptic Equations in a Ball, J. Differential Equations 138 (1997) 351-379. | MR 1462272 | Zbl 0884.34025

[10] Franchi B., Lanconelli E., Serrin J., Existence and Uniqueness of Nonnegative Solutions of Quasilinear Equations in ${R}^{n}$, Adv. Math. 118 (1996) 177-243. | MR 1378680 | Zbl 0853.35035

[11] García-Huidobro M., Henao D., On the Uniqueness of Positive Solutions of a Quasilinear Equation Containing a Weighted P-Laplacian, Comm. Contemp. Math. 10 (2008) 405-432. | MR 2417923 | Zbl pre05315913

[12] Kwong M. K., Uniqueness of Positive Solutions of $\Delta u-u+{u}^{p}=0$, Arch. Ration. Mech. Anal. 105 (1989) 243-266. | MR 969899 | Zbl 0676.35032

[13] Mcleod K., Uniqueness of Positive Radial Solutions of $\Delta u+f\left(u\right)=0$ in ${R}^{N}$, II, Trans. Amer. Math. Soc. 339 (1993) 495-505. | MR 1201323 | Zbl 0804.35034

[14] Mcleod K., Serrin J., Uniqueness of Positive Radial Solutions of $\Delta u+f\left(u\right)=0$ in ${R}^{N}$, Arch. Ration. Mech. Anal. 99 (1987) 115-145. | MR 886933 | Zbl 0667.35023

[15] Mcleod K., Troy W. C., Weissler F. B., Radial Solutions of $\Delta u+f\left(u\right)=0$ With Prescribed Numbers of Zeros, J. Differential Equations 83 (2) (1990) 368-378. | MR 1033193 | Zbl 0695.34020

[16] Peletier L., Serrin J., Uniqueness of Positive Solutions of Quasilinear Equations, Arch. Ration. Mech. Anal. 81 (1983) 181-197. | MR 682268 | Zbl 0516.35031

[17] Peletier L., Serrin J., Uniqueness of Nonnegative Solutions of Quasilinear Equations, J. Differential Equations 61 (1986) 380-397. | MR 829369 | Zbl 0577.35035

[18] Pucci P. R., Serrin J., Uniqueness of Ground States for Quasilinear Elliptic Operators, Indiana Univ. Math. J. 47 (1998) 529-539. | MR 1647928 | Zbl 0920.35055

[19] Serrin J., Tang M., Uniqueness of Ground States for Quasilinear Elliptic Equations, Indiana Univ. Math. J. 49 (2000) 897-923. | MR 1803216 | Zbl 0979.35049

[20] Troy W., The Existence and Uniqueness of Bound State Solutions of a Semilinear Equation, Proc. Roy Soc. A 461 (2005) 2941-2963. | MR 2165520 | Zbl pre05213391