This paper deals with the following nonlinear equations Mλ,Λ ±(D2u)+g(u)=0inRN,where Mλ,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.
Oscillating solutions for nonlinear equations involving the Pucci's extremal operators / D'Avenia, Pietro; Pomponio, Alessio. - In: NONLINEAR ANALYSIS: REAL WORLD APPLICATIONS. - ISSN 1468-1218. - STAMPA. - 55:(2020). [10.1016/j.nonrwa.2020.103118]
Oscillating solutions for nonlinear equations involving the Pucci's extremal operators
d'Avenia, Pietro
;Pomponio, Alessio
2020-01-01
Abstract
This paper deals with the following nonlinear equations Mλ,Λ ±(D2u)+g(u)=0inRN,where Mλ,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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
