Abstract
We shall consider here the question of existence and nonexistence of ground states for the prescribed mean curvature equation in ℝn (n > 2), that is, we consider solutions of the problem
where Du denotes the gradient of u. The function f(u), defined for u > 0, will be assumed throughout to satisfy the following hypotheses:
(H2) f(0) = 0, and there exists a number a ≥ 0 such that
if a > 0 we require
.
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Atkinson, F.V., Peletier, L.A., Serrin, J. (1988). Ground States for the Prescribed Mean Curvature Equation: The Supercritical Case. In: Ni, WM., Peletier, L.A., Serrin, J. (eds) Nonlinear Diffusion Equations and Their Equilibrium States I. Mathematical Sciences Research Institute Publications, vol 12. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9605-5_4
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DOI: https://doi.org/10.1007/978-1-4613-9605-5_4
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