Monotonicity of the Morse index of radial solutions of the Hénon equation in dimension two

Publication date: August 2019Source: Nonlinear Analysis: Real World Applications, Volume 48Author(s): Wendel Leite da Silva, Ederson Moreira dos SantosAbstractWe consider the equation −Δu=|x|α|u|p−1u,x∈B,u=0on∂B,where B⊂R2 is the unit ball centered at the origin, α≥0, p>1, and we prove some results on the Morse index of radial solutions. The contribution of this paper is twofold. Firstly, fixed the number of nodal sets n≥1 of the solution uα,n, we prove that the Morse index m(uα,n) is monotone non-decreasing with respect to α. Secondly, we provide a lower bound for the Morse indices m(uα,n), which shows that m(uα,n)→+∞ as α→+∞.

Source: Nonlinear Analysis: Real World Applications - February 28, 2019 Category: Research Source Type: research