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Tempered fractional differential equation: variational approach
Author(s) -
Torres César
Publication year - 2017
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.4361
Subject(s) - mathematics , nehari manifold , sobolev space , fractional calculus , mathematical analysis , ground state , state (computer science) , mountain pass theorem , pure mathematics , physics , algorithm , quantum mechanics , nonlinear system
In this paper, we are concerned with the existence of ground state solution for the following fractional differential equations with tempered fractional derivative: FDD − α , λ ( D + α , λ u ( t ) ) = f ( t , u ( t ) ) ,t ∈ Ru ∈ W α , 2 ( R ) ,where α ∈(1/2,1), λ >0,D ± α , λ u are the left and right tempered fractional derivatives,W α , 2 ( R ) is the fractional Sobolev spaces, and f ∈ C ( R × R , R ) . Assuming that f satisfies the Ambrosetti–Rabinowitz condition and another suitable conditions, by using mountain pass theorem and minimization argument over Nehari manifold, we show that (FD) has a ground state solution. Furthermore, we show that this solution is a radially symmetric solution. Copyright © 2017 John Wiley & Sons, Ltd.