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Uniqueness of positive solutions of semilinear equations in \(R^ n\). (English) Zbl 0516.35031

MSC:
35J65 Nonlinear boundary value problems for linear elliptic equations
35J25 Boundary value problems for second-order elliptic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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[2] Berestycki, H., & P. L. Lions, Existence of a ground state in nonlinear equations of the type Klein-Gordon, in Variational Inequalities. (Cottle, Gianesi and J.-L. Lions, editors). New York: J. Wiley, 1980. · Zbl 0707.35143
[3] Berestycki, H., Lions, P. L., & L. A. Peletier, An ODE approach to the existence of positive solutions for semilinear problems in \(\mathbb{R}\)n, Indiana University Math. Jour. 30, 141–157 (1981). · Zbl 0522.35036
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[6] Coffman, C. V., Uniqueness of the ground state so · Zbl 0249.35029
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[8] Fisher, R. A., The wave of advance of advantageous genes, Jour. of Eugenics 7, 355–369 (1937). · JFM 63.1111.04
[9] Gidas, B., Ni, W.-M., & L. Nirenberg, Symmetry of positive solutions of nonlinear elliptic equations in \(\mathbb{R}\)n. Commun. Math. Phys. 68, 209–243 (1979). · Zbl 0425.35020
[10] Jones, C. K. R. T., Spherically symmetric waves of a reaction-diffusion equation, MRC Technical Summary Report #2046, 1979.
[11] McLeod, K., & J. Serrin, Uniqueness of the ground state solution for {\(\Delta\)}u + f(u) = 0. Proc. Nat. Acad. Sci. USA, 78, 6592–6595 (1981). · Zbl 0474.35047
[12] Serrin, J., Phase transitions and interfacial layers for van der Waals fluids, in Recent Methods in Nonlinear Analysis and Applications: Proceedings of the Fourth International Meeting of SAFA, eds. Canfora, A., Rionero, F., Sbordone, C. & Trombetti, G. (Liquori Editore, Naples, Italy), pp. 169–175 (1980).
[13] Van Der Waals, J. D., & R. Kohnstamm, Lehrbuch der Thermodynamik, vol. 1. Leipzig, 1908.
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