期刊
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
卷 27, 期 1-3, 页码 314-327出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2015.02.019
关键词
Liouville-Weyl fractional derivative; Fractional Sobolev space; Critical point theory; Comparison argument
We study the existence of positive solution for the one dimensional Schrodinger equation with mixed Liouville-Weyl fractional derivatives tD(infinity)(proportional to)((-infinity)D(t)(proportional to)u(t)) + B(t)u(t) = f(u(t)), t is an element of R u is an element of H-proportional to(R). Furthermore, we analyse radial symmetry property of these solutions. The proof is carried out by using variational methods jointly with comparison and rearrangement argument. (C) 2015 Published by Elsevier B.V.
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