Premium
Ground state solution for differential equations with left and right fractional derivatives
Author(s) -
Torres César
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3426
Subject(s) - mathematics , argument (complex analysis) , class (philosophy) , work (physics) , state (computer science) , differential equation , ground state , fractional calculus , pure mathematics , mathematical analysis , algorithm , engineering , mechanical engineering , biochemistry , chemistry , physics , quantum mechanics , artificial intelligence , computer science
In this work, we study the existence of positive solutions for a class of fractional differential equation given by 1tD ∞ α− ∞D t α u ( t ) + u ( t ) = f ( t , u ( t ) ) ,u ∈ H α ( R ) ,where α ∈ ( 1 / 2 , 1 ) , t ∈ R , u ∈ R , f ∈ C ( R , R ) . Using the mountain pass theorem and comparison argument, we prove that (1) at least has one nontrivial solution. Copyright © 2015 John Wiley & Sons, Ltd.