TY - JOUR
T1 - A supercritical scalar field equation with a forcing term
AU - Ishige, Kazuhiro
AU - Okabe, Shinya
AU - Sato, Tokushi
N1 - Funding Information:
The first author was partially supported by the Grant-in-Aid for Scientific Research (A) (No. 15H02058 ) from Japan Society for the Promotion of Science .
Publisher Copyright:
© 2019
PY - 2019/8
Y1 - 2019/8
N2 - This paper is concerned with the elliptic problem for a scalar field equation with a forcing term −Δu+u=up+κμ in RN, where N≥2, p>1, κ>0 and μ is a Radon measure in RN with a compact support. Under a suitable integrability condition on μ, we give a complete classification of the existence and nonexistence of positive solutions decaying at the space infinity in the case of 1JL. Here pJL is the so-called Joseph-Lundgren exponent.
AB - This paper is concerned with the elliptic problem for a scalar field equation with a forcing term −Δu+u=up+κμ in RN, where N≥2, p>1, κ>0 and μ is a Radon measure in RN with a compact support. Under a suitable integrability condition on μ, we give a complete classification of the existence and nonexistence of positive solutions decaying at the space infinity in the case of 1JL. Here pJL is the so-called Joseph-Lundgren exponent.
KW - Scalar field equation
KW - Supercritical
KW - The Joseph-Lundgren exponent
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U2 - 10.1016/j.matpur.2019.04.003
DO - 10.1016/j.matpur.2019.04.003
M3 - Article
AN - SCOPUS:85063881466
SN - 0021-7824
VL - 128
SP - 183
EP - 212
JO - Journal des Mathematiques Pures et Appliquees
JF - Journal des Mathematiques Pures et Appliquees
ER -