Existence and nonexistence of positive solutions to some fully nonlinear equation in one dimension

Patricio Felmer, Norihisa Ikoma

Research output: Contribution to journalArticle

Abstract

In this paper, we consider the existence (and nonexistence) of solutions to −Mλ,Λ ±(u)+V(x)u=f(u)inR where Mλ,Λ + and Mλ,Λ denote the Pucci operators with 0<λ≤Λ<∞ V(x) is a bounded function, f(s) is a continuous function and its typical example is a power-type nonlinearity f(s)=|s|p−1s (p>1). In particular, we are interested in positive solutions which decay at infinity, and the existence (and nonexistence) of such solutions is proved.

Original languageEnglish
Pages (from-to)2162-2196
Number of pages35
JournalJournal of Functional Analysis
Volume275
Issue number8
DOIs
Publication statusPublished - 2018 Oct 15

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Fully Nonlinear Equations
One Dimension
Nonexistence
Positive Solution
Infinity
Decay
Denote
Operator

Keywords

  • Leray–Schauder degree
  • Positive solutions
  • Pucci operators

ASJC Scopus subject areas

  • Analysis

Cite this

Existence and nonexistence of positive solutions to some fully nonlinear equation in one dimension. / Felmer, Patricio; Ikoma, Norihisa.

In: Journal of Functional Analysis, Vol. 275, No. 8, 15.10.2018, p. 2162-2196.

Research output: Contribution to journalArticle

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