TY - JOUR
T1 - Existence of solutions of scalar field equations with fractional operator
AU - Ikoma, Norihisa
N1 - Publisher Copyright:
© 2016, Springer International Publishing.
PY - 2017/3/1
Y1 - 2017/3/1
N2 - In this paper, the existence of least energy solution and infinitely many solutions is proved for the equation (1 - Δ) αu= f(u) in RN where 0 < α< 1 , N≥ 2 and f(s) is a Berestycki–Lions type nonlinearity. The characterization of the least energy by the mountain pass value is also considered and the existence of optimal path is shown. Finally, exploiting these results, the existence of positive solution for the equation (1 - Δ) αu= f(x, u) in RN is established under suitable conditions on f(x, s).
AB - In this paper, the existence of least energy solution and infinitely many solutions is proved for the equation (1 - Δ) αu= f(u) in RN where 0 < α< 1 , N≥ 2 and f(s) is a Berestycki–Lions type nonlinearity. The characterization of the least energy by the mountain pass value is also considered and the existence of optimal path is shown. Finally, exploiting these results, the existence of positive solution for the equation (1 - Δ) αu= f(x, u) in RN is established under suitable conditions on f(x, s).
KW - Mountian pass theorem
KW - Symmetric mountain pass theorem
KW - The Pohozaev identity
KW - Variational method
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U2 - 10.1007/s11784-016-0369-x
DO - 10.1007/s11784-016-0369-x
M3 - Article
AN - SCOPUS:84995427031
SN - 1661-7738
VL - 19
SP - 649
EP - 690
JO - Journal of Fixed Point Theory and Applications
JF - Journal of Fixed Point Theory and Applications
IS - 1
ER -