References
Bénilan, P., Brézis, H., Crandall, M.G.: A semilinear equation inL 1(R N). Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser.2, 523–555 (1975)
Berestycki, H., Lions, P.L.: Nonlinear scalar field equations I, II. Arch. Ration. Mech. Anal.82, 313–345, 347–375 (1983)
Berger, M.S.: On the existence and structure of stationary states for a nonlinear Klein-Gordon equations. J. Funct. Anal.9, 249–261 (1972)
Coffman, C.V.: Uniqueness of the ground state solution for Δu−u+u 3=0 and a variational characterization of other solutions. Arch. Ration. Mech. Anal.46, 81–95 (1972)
Fugakai, N.: Existence and uniqueness of entire solutions of second order sublinear elliptic equations. Funkc. Ekvacioj, Ser. Int. (to appear)
Ince, E.I.: Ordinary differential equations. New York: Dover 1956
Kusano, T., Swanson, C.A.: Asymptotic properties of semilinear elliptic equations. Funkc. Ekvacioj, Ser. Int.26, 115–129 (1983)
Kusano, T., Swanson, C.A.: Asymptotic theory of singular semilinear elliptic equations. Can. Math. Bull.27, 223–232 (1984)
Kusano, T., Swanson, C.A.: Growth properties of stationary Klein-Gordon equations. SIAM J. Math. Anal.16, 440–446 (1985)
Kusano, T., Swanson, C.A.: Unbounded positive entire solutions of semilinear elliptic equations. Nonlinear Anal., Theory Methods Appl. (to appear)
McLeod, K., Serrin, J.: Uniqueness of solutions of semilinear Poisson equations. Proc. Natl. Acad. Sci. USA78, 6592–6595 (1981)
Nehari, Z.: On a linear differential equation arising in nuclear physics. Proc. R. Ir. Acad., Sect. A62, 117–135 (1963)
Ni, W.-M.: On the elliptic equationΔu+K(x)u (n+2)/(n−2)=0, its generalizations, and applications in geometry. Indiana Univ. Math. J.31, 493–529 (1982)
Ni, W.-M.: On the positive radial solutions of some semilinear elliptic equations onR n. Appl. Math. Optimization9, 373–380 (1983)
Noussair, E.S.: On the existence of solutions of nonlinear elliptic boundary value problems. J. Differ. Equations34, 482–495 (1979)
Noussair, E.S., Swanson, C.A.: Positive solutions of quasilinear elliptic equations in exterior domains. J. Math. Anal. Appl.75, 121–133 (1980)
Noussair, E.S., Swanson, C.A.: Existence theorems for generalized Klein-Gordon equations. Bull. Am. Math. Soc., New Ser.8, 333–336 (1983)
Noussair, E.S., Swanson, C.A.: Global positive solutions of semilinear elliptic problems. Pac. J. Math.115, 177–192 (1984)
Noussair, E.S., Swanson, C.A.: Positive solutions of semilinear elliptic problems in unbounded domains. J. Differ. Equations57, 349–372 (1985)
Peletier, L.A., Serrin, J.: Uniqueness of positive solutions of semilinear equations inR n. Arch. Ration. Mech. Anal.81, 181–197 (1983)
Strauss, W.A.: Existence of solitary waves in higher dimensions. Commun. Math. Phys.55, 149–162 (1977)
Toland, J.F.: Positive solutions of nonlinear elliptic equations-existence and nonexistence of solutions with radial symmetry inL p(R N). Trans. Am. Math. Soc.282, 335–354 (1984)
Watson, G.N.: A treatise on the theory of Bessel functions. London: Cambridge 1944
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Fukagai, N. Positive entire solutions of semilinear elliptic equations. Math. Ann. 274, 75–93 (1986). https://doi.org/10.1007/BF01458018
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DOI: https://doi.org/10.1007/BF01458018