Monotonicity properties for ground states of the scalar field equation

Felmer, Patricio L.; Quaas, Alexander; Tang, Moxun; Yu, Jianshe

doi:10.1016/j.anihpc.2006.12.003

Felmer, Patricio L. ; Quaas, Alexander ; Tang, Moxun ; Yu, Jianshe

Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 1, pp. 105-119.

MR Zbl

DOI : 10.1016/j.anihpc.2006.12.003

@article{AIHPC_2008__25_1_105_0,
     author = {Felmer, Patricio L. and Quaas, Alexander and Tang, Moxun and Yu, Jianshe},
     title = {Monotonicity properties for ground states of the scalar field equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {105--119},
     publisher = {Elsevier},
     volume = {25},
     number = {1},
     year = {2008},
     doi = {10.1016/j.anihpc.2006.12.003},
     mrnumber = {2383080},
     zbl = {1136.35032},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2006.12.003/}
}

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Felmer, Patricio L.; Quaas, Alexander; Tang, Moxun; Yu, Jianshe. Monotonicity properties for ground states of the scalar field equation. Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 1, pp. 105-119. doi : 10.1016/j.anihpc.2006.12.003. http://www.numdam.org/articles/10.1016/j.anihpc.2006.12.003/

Bibliographie
Cité par

[1] Berestycki H., Lions P.L., Nonlinear scalar field equations. I. Existence of a ground state, Arch. Rational Mech. Anal. 82 (1983) 313-345. | MR | Zbl

[2] Chen C.C., Lin C.S., Uniqueness of the ground state solutions of $Δ u + f (u) = 0$ in $R^{n}$ , $n \geq 3$ , Comm. Partial Differential Equations 16 (1991) 1549-1572. | MR | Zbl

[3] Coffman C., On the positive solutions of boundary problems for a class of nonlinear differential equations, J. Differential Equations 3 (1967) 92-111. | MR | Zbl

[4] Cortázar C., Elgueta M., Felmer P., Uniqueness of positive solutions of $Δ u + f (u) = 0$ in $R^{N}$ , $N \geq 3$ , Arch. Rational Mech. Anal. 142 (1998) 127-141. | MR | Zbl

[5] Felmer P.L., Quaas A., On critical exponents for the Pucci's extremal operators, Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (2003) 843-865. | Numdam | MR

[6] Felmer P., Quaas A., Tang M., On uniqueness for a nonlinear elliptic equation involving the Pucci's extremal operator, J. Differential Equations 226 (2006) 80-98. | MR

[7] Gidas B., Ni W.M., Nirenberg L., Symmetry of positive solutions of nonlinear elliptic equations in $R^{n}$ , in: Mathematical Analysis and Applications, Part A, Adv. in Math. Suppl. Stud., vol. 7a, Academic Press, New York, 1981, pp. 369-402. | MR | Zbl

[8] Kwong M.K., Uniqueness of positive solutions of $Δ u - u + u^{p} = 0$ in $R^{n}$ , Arch. Rational Mech. Anal. 105 (1989) 243-266. | MR | Zbl

[9] Kwong M.K., Zhang L., Uniqueness of the positive solution of $Δ u + f (u) = 0$ in an annulus, Differential Integral Equations 4 (1991) 583-596. | MR | Zbl

[10] Mcleod K., Serrin J., Uniqueness of positive radial solutions of $Δ u + f (u) = 0$ in $R^{n}$ , Arch. Rational Mech. Anal. 99 (1987) 115-145. | MR | Zbl

[11] Mcleod K., Uniqueness of positive radial solutions of $Δ u + f (u) = 0$ in $R^{n}$ , II, Trans. Amer. Math. Soc. 339 (1993) 495-505. | MR | Zbl

[12] Ni W.M., Uniqueness of solutions of nonlinear Dirichlet problems, J. Differential Equations 50 (1983) 289-304. | MR | Zbl

[13] Ni W.M., Nussbaum R., Uniqueness of nonuniqueness for positive radial solutions of $Δ u + f (u, r) = 0$ , Comm. Pure Appl. Math. 38 (1985) 67-108. | MR | Zbl

[14] Peletier L.A., Serrin J., Uniqueness of positive solutions of semilinear equations in $R^{N}$ , Arch. Rational Mech. Anal. 81 (1983) 181-197. | MR | Zbl

[15] Peletier L.A., Serrin J., Uniqueness of non-negative of semilinear equations in $R^{N}$ , solutions of semilinear equations in $R^{N}$ , J. Differential Equations 61 (1986) 380-397. | MR | Zbl

[16] Pohozaev S.I., On the eigenfunctions of the equation $Δ u + λ f (u) = 0$ , Dokl. Akad. Nauk SSSR 165 (1965) 36-39, (in Russian). | MR | Zbl

[17] Serrin J., Tang M., Uniqueness of ground states for quasilinear elliptic equations, Indiana Univ. Math. J. 49 (2000) 897-923. | MR | Zbl

[18] Tang M., Uniqueness and global structure of positive radial solutions for quasilinear elliptic equations, Comm. Partial Differential Equations 26 (2001) 909-938. | MR | Zbl

[19] Tang M., Uniqueness of positive radial solutions for $Δ u - u + u^{p} = 0$ on an annulus, J. Differential Equations 189 (2003) 148-160. | MR | Zbl

[20] Tang M., Exact multiplicity for semilinear elliptic Dirichlet problems involving concave and convex nonlinearities, Proc. Roy. Soc. Edinburgh Sect. A 133 (2003) 705-717. | MR | Zbl

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