Ground states for the prescribed mean curvature equation
Authors:
L. A. Peletier and J. Serrin
Journal:
Proc. Amer. Math. Soc. 100 (1987), 694700
MSC:
Primary 35J65; Secondary 53A10
MathSciNet review:
894440
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Abstract 
References 
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Abstract: We discuss the existence of radial ground states of problem , under appropriate restrictions on the bifurcation parameter and the exponent .
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29 (1968), 125–143. MR 0223638
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McLeod and James
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equations, Proc. Nat. Acad. Sci. U.S.A. 78 (1981),
no. 11, 6592–6595. MR 634934
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physics, Proc. Roy. Irish Acad. Sect. A 62 (1963),
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W.M. Ni and J. Serrin, Nonexistence theorems for quasilinear partial differential equations, Rend. Circ. Mat. Palermo (2) 5 (1986).
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, Existence and nonexistence theorems for ground states of quasilinear partial differential equations. The anomalous case, Accad. Naz. Lincei. (in press).
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A. Peletier and James
Serrin, Uniqueness of positive solutions of semilinear equations in
𝑅ⁿ, Arch. Rational Mech. Anal. 81
(1983), no. 2, 181–197. MR 682268
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 [1]
 F. V. Atkinson and L. A. Peletier, Ground states of and the EmdenFowler equation, Arch. Rational Mech. Anal. 93 (1986), 103127. MR 823114 (87h:35105)
 [2]
 H. Berestycki and P.L. Lions, Nonlinear scalar field equations. I, Arch. Rational Mech. Anal. 82 (1983), 313345. MR 695535 (84h:35054a)
 [3]
 H. Berestycki, P.L. Lions, and L. A. Peletier, An ODE approach to the existence of positive solutions for semilinear problems in , Indiana Univ. Math. J. 30 (1981), 141157. MR 600039 (83e:35009)
 [4]
 P. Concus and R. Finn, A singular solution of the capillary equation. I, II, Invent. Math. 29 (1975), 143148, 149159.
 [5]
 T. K. Evers, Numerical search for ground state solutions of a modified capillary equation, M. Sc. Thesis, Dept. of Math., Iowa State Univ., 1985.
 [6]
 R. Finn, On the behaviour of a capillary surface near a singular point, J. Analyse Math. 30 (1976), 156163. MR 0435996 (55:8947)
 [7]
 R. H. Fowler, Further studies of Emden's and similar differential equations, Quart. J. Math. Oxford Ser. (2) 2 (1931), 259288.
 [8]
 B. Franchi, E. Lanconelli, and J. Serrin, Esistenza e unicitá degli stati fondamentali per equazoni ellitici quasilineari, Rend. Accad. Naz. Lincei. (in press).
 [9]
 W. E. Johnson and L. M. Perko, Interior and exterior boundary value problems from the theory of the capillary tube, Arch. Rational Mech. Anal. 29 (1968), 129143. MR 0223638 (36:6686)
 [10]
 K. McLeod and J. Serrin, Uniqueness of the ground state solution for , Proc. Nat. Acad. Sci. U.S.A. 78 (1981), 65926595. MR 634934 (82k:35029)
 [11]
 Z. Nehari, On a nonlinear differential equation arising in nuclear physics, Proc. Roy. Irish Acad. 62 (1963), 117135. MR 0165176 (29:2465)
 [12]
 W.M. Ni and J. Serrin, Nonexistence theorems for quasilinear partial differential equations, Rend. Circ. Mat. Palermo (2) 5 (1986).
 [13]
 , Existence and nonexistence theorems for ground states of quasilinear partial differential equations. The anomalous case, Accad. Naz. Lincei. (in press).
 [14]
 L. A. Peletier and J. Serrin, Uniqueness of positive solutions of semilinear equations in , Arch. Rational Mech. Anal. 81 (1983), 181197. MR 682268 (84b:35046)
 [15]
 , Uniqueness of nonnegative solutions of semilinear equations in , J. Differential Equations 61 (1986), 380397.
 [16]
 W. A. Strauss, Existence of solitary waves in higher dimensions, Comm. Math. Phys. 55 (1977), 149162. MR 0454365 (56:12616)
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DOI:
http://dx.doi.org/10.1090/S00029939198708944408
PII:
S 00029939(1987)08944408
Article copyright:
© Copyright 1987
American Mathematical Society
