Browsing by Subject "POSITIVE SOLUTIONS"

Sort by: Order: Results:

Now showing items 1-2 of 2
  • Bonheure, Denis; Casteras, Jean-Baptiste; Foldes, Juraj (2020)
    We study singular radially symmetric solution of the stationary Keller-Segel equation, that is, an elliptic equation with exponential nonlinearity, which is supercritical in dimension N >= 3. The solutions are unbounded at the origin and we show that they describe the asymptotics of bifurcation branches of regular solutions. It is shown that for any ball and any k >= 0, there is a singular solution that satisfies Neumann boundary condition and oscillates at least k times around the constant equilibrium. Moreover, we prove that in dimension 3 10, we show that the Morse index of the singular solution is finite, and therefore the existence of regular solutions with fast oscillations is not expected. (C) 2019 Elsevier Masson SAS. All rights reserved.
  • Casteras, Jean-Baptiste; Földes, Juraj (2020)
    We study singular radially symmetric solution to the Lin-Ni-Takagi equation for a supercritical power non-linearity in dimension N >= 3. It is shown that for any ball and any k >= 0, there is a singular solution that satisfies Neumann boundary condition and oscillates at leastktimes around the constant equilibrium. Moreover, we show that the Morse index of the singular solution is finite or infinite if the exponent is respectively larger or smaller than the Joseph-Lundgren exponent.