Oscillating solutions for nonlinear equations involving the Pucci's extremal operators. (October 2020) - d'Avenia, Pietro; Pomponio, Alessio
Abstract: This paper deals with the following nonlinear equations M λ, Λ ± ( D 2 u ) + g ( u ) = 0 i n 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 .