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

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...

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Bibliographic Details
Published in:Nonlinear analysis: real world applications 2020-10, Vol.55, p.103118, Article 103118
Main Authors: d’Avenia, Pietro, Pomponio, Alessio
Format: Article
Language:English
Subjects:
Fully nonlinear operator equations
Mathematical analysis
Nonlinear equations
Operators
Oscillating solutions
Pucci’s extremal operators
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Summary: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.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2020.103118