Abstract
We study the existence and behavior of positive radial solutions of the equationΔu + f(u) = 0 in ℝn. This equation arises in various problems in applied mathematics, e.g. in the study of phase transitions, nuclear cores and more recently in population genetics and solitary waves. The important model casef(u) = − u + u p, p>1, describes for instance the pressure distribution in a van der Waals fluid. In this case, we obtain fairly complete knowledge of all positive radial solutions.
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Communicated by D. Kinderlehrer
Supported in part by an NSF grant and a research grant from the Graduate School of the University of Minnesota.
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Ni, WM. On the positive radial solutions of some semilinear elliptic equations on ℝn . Appl Math Optim 9, 373–380 (1982). https://doi.org/10.1007/BF01460131
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DOI: https://doi.org/10.1007/BF01460131