Oscillating solutions for nonlinear equations involving the Pucci's extremal operators

2019/04/26 by d'Avenia, Pietro, Pomponio, Alessio
#35B05 #35J6 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1904.12001

Abstract

This paper deals with the following nonlinear equations M_λ,Λ^±(D² u)+g(u)=0 \hbox in ℝ^N, where M_λ,Λ^± are the Pucci's extremal operators, for N ≥ 1 and under the assumption g'(0)>0. We show the existence of oscillating solutions, namely with an unbounded sequence of zeros. Moreover these solutions are periodic, if N=1, while they are radial symmetric and decay to zero at infinity with their derivatives, if N≥ 2.

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