TY - JOUR
T1 - Existence and nonexistence of positive solutions to some fully nonlinear equation in one dimension
AU - Felmer, Patricio
AU - Ikoma, Norihisa
N1 - Funding Information:
The authors would like to express their sincere gratitude to an anonymous referee for his/her careful reading and comments to improve the presentation of this paper. The authors would like to thank Lawrence Evans for pointing up the variational structure of (1.1). P.F. was partially supported BASAL-CMM projects. N.I. was partially supported by JSPS Research Fellowships 24-2259 and JSPS KAKENHI Grant Number JP16K17623. The second author would like to thank Universidad de Chile, where this work was started, for their hospitality.
Funding Information:
The authors would like to express their sincere gratitude to an anonymous referee for his/her careful reading and comments to improve the presentation of this paper. The authors would like to thank Lawrence Evans for pointing up the variational structure of (1.1) . P.F. was partially supported BASAL-CMM projects. N.I. was partially supported by JSPS Research Fellowships 24-2259 and JSPS KAKENHI Grant Number JP16K17623 . The second author would like to thank Universidad de Chile, where this work was started, for their hospitality.
Publisher Copyright:
© 2018 Elsevier Inc.
PY - 2018/10/15
Y1 - 2018/10/15
N2 - 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.
AB - 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.
KW - Leray–Schauder degree
KW - Positive solutions
KW - Pucci operators
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U2 - 10.1016/j.jfa.2018.07.009
DO - 10.1016/j.jfa.2018.07.009
M3 - Article
AN - SCOPUS:85050406660
SN - 0022-1236
VL - 275
SP - 2162
EP - 2196
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 8
ER -