An upper bound for the least energy of a sign-changing solution to a zero mass problem

2022/09/21 by Clapp, Mónica, Maia, Liliane A., Pellacci, Benedetta · 1 citation
#35B06 #35B08 #35B45 #35J20 #35J61 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.10706

Abstract

We give an upper bound for the least energy of a sign-changing solution to the the nonlinear scalar field equation -Δu = f(u), u∈ D^1,2(ℝ^N), where N≥5 and the nonlinearity f is subcritical at infinity and supercritical near the origin. More precisely, we establish the existence of a nonradial sign-changing solution whose energy is smaller that 12c₀ if N=5,6 and smaller than 10c₀ if N≥ 7, where c₀ is the ground state energy.

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• Multiple nodal solutions to a scalar field equation with double-power nonlinearity and zero mass at infinity

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