References
Berestycki, H., Lions, P.L.: Nonlinear scalar field equations. I, II. Arch. Rat. Mech. Anal.82, 313–345, 347–375 (1983)
Berestycki, H., Lions, P.L., Peletier, L.A.: An ODE approach to the existence of positive solutions for semilinear problems inR N. Indiana Univ. Math. J.30, 141–157 (1981)
Kawano, N.: On bounded entire solutions of semilinear elliptic equations. Hiroshima Math. J.14 (1984)
Kawano, N., Kusano, T., Naito, M.: On the elliptic equation Δu=ϕ(x)u γ inR 2. Proc. Am. Math. Soc.
Kusano, T., Oharu, S.: Bounded entire solutions of second order semilinear elliptic equations with application to a parabolic initial value problem. Indiana Univ. Math. J.
Kusano, T., Oharu, S.: On entire solutions of second order semilinear elliptic equations. Submitted for publication
Ni, W.M.: On the elliptic equation Δu+K(x)u (n+2)/(n−2)=0, its generalizations, and its applications in geometry. Indiana Univ. Math. J.31, 493–529 (1982)
Ni, W.M.: On the elliptic equation Δu+K(x)e 2u=0 and conformal metrics with prescribed Gaussian curvatures. Invent. Math.66, 343–352 (1982)
Noussair, E.S., Swanson, C.A.: Positive solutions of quasilinear elliptic equations in exterior domains. J. Math. Anal. Appl.75, 121–133 (1980)
Walter, W.: Entire solutions of the differential equation Δu=f(u). J. Austral. Math. Soc. (Ser. A)30, 366–368 (1981)
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Supported in part by Grant-in-Aid for Scientific Research (No. 58460004), Ministry of Education, Japan
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Kusano, T., Usami, H. Positive solutions of a class of second order semilinear elliptic equations in the plane. Math. Ann. 268, 255–264 (1984). https://doi.org/10.1007/BF01456089
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DOI: https://doi.org/10.1007/BF01456089