This is a preview of subscription content, log in via an institution to check access.
Bibliography
Atkinson, F. V. & Peletier, L. A., Ground states of -Δu=f(u) and the Emden-Fowler Equation, Arch. Rational Mech. Analysis 93, 103–127 (1986).
Berestycki, H. & Lions, P.-L., Non-linear scalar field equations I, Existence of a ground state; II, Existence of infinitely many solutions, Arch. Rational Mech. Analysis 82, 313–375 (1983).
Berestycki, H., Lions, P.-L. & Peletier, L. A., An ODE approach to the existence of positive solutions for semilinear problems in ℝn, Indiana University Math. J. 30, 141–167 (1981).
Bongiorno, V., Scriven, L. E. & Davies, H. T., Molecular theory of fluid interfaces, J. Colloid and Interface Science 57, 462–475 (1967).
Coffman, C. V., Uniqueness of the ground state solution for Δu−u+u 3=0 and a variational characterization of other solutions, Arch. Rational Mech. Analysis 46, 12–95 (1972).
Diaz, J. I., Nonlinear partial differential equations and free boundaries, Vol. I. Elliptic Equations. Research Notes, 106. Pitman, London (1985).
Fife, P. C., Mathematical aspects of reacting and diffusing systems, Lecture notes in Biomathematics 28, Springer-Verlag (1979).
Finkelstein, R., Lelevier, R. & Ruderman, M., Non-linear spinor fields, Phys. Rev. 83, 326–332 (1951).
Fisher, R. A., The wave of advance of advantageous genes, J. of Eugenics 7, 355–369 (1937).
Gidas, B., Ni, W.-M. & Nirenberg, L., Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68, 209–243 (1979).
Gidas, B., Ni, W.-M. & Nirenberg, L., Symmetry of positive solutions of nonlinear elliptic equations in ℝn, Math. Anal. Appl. Part A. 7A, 369–402 (1981).
Macki, J. W., A singular nonlinear boundary value problem, Pac. J. Math. 78, 375–383 (1978).
Nehari, A., On a nonlinear differential equation arising in nuclear physics, Proc. R. Irish Acad. Sect. A 62, 117–135 (1963).
Ni, W.-M., On the positive radial solutions of some semilinear elliptic equations on ℝn, Appl. Math. Optim. 9, 373–380 (1983).
Ni, W.-M. & Nussbaum, R., Uniqueness and non-uniqueness of positive radial solutions of Δu+f(u, r)=0. Comm. Pure Appl. Math. 38. 67–108 (1985).
Peletier, L. A. & Serrin, J., Uniqueness of positive solutions of semilinear equations in ℝn, Arch. Rational Mech. Analysis 81, 181–197 (1983).
Peletier, L. A. & Serrin, J., Uniqueness of non-negative solutions of semilinear equations in ℝn, J. Differential Equations 6, 380–397 (1986).
Sansone, G., Su un'equazione differenziale non lineare della fisica nucleare, Symp. Math. 6, 5–139 (1970).
Serrin, J., Phase transitions and interfacial layers for van der Waals fluids, in Recent Methods in Nonlinear Analysis und Applications; eds. Canfora, A., Rionero, S., Sbordone, C. and Trombetti, G. Liguori Editore, Naples.
Strauss, W. A., Existence of solitary waves in higher dimensions, Comm. Math. Phys. 55, 149–162 (1977).
Synge, J. L., On a certain non linear differential equation, Proc. R. Irish Acad. Sect. A 62, 19–41 (1961).
Takahashi, Y., The structure of the nucleon core by the Hartree approximations, Nucl. Phys. 26, 658–669 (1961).
van der Waals, J. D. & Kohnstamm, R., Lehrbuch der Thermodynamik, vol. 1, Leipzig (1908).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
McLeod, K., Serrin, J. Uniqueness of positive radial solutions of Δu+f(u)=0 in ℝn . Arch. Rational Mech. Anal. 99, 115–145 (1987). https://doi.org/10.1007/BF00275874
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00275874