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Title: On fractional Schro{sup ¨}dinger equation in R{sup N} with critical growth

In this paper, we study the following nonlinear fractional Schro{sup ¨}dinger equation with critical exponent h{sup 2α}(−Δ){sup α}u+V(x)u=|u|{sup 2{sub α}{sup *−2}}u+λ|u|{sup q−2}u,x∈R{sup N}, where h is a small positive parameter, 0 < α < 1, 2 2α, λ > 0 is a parameter. The potential V:R{sup N}→R is a positive continuous function satisfying some natural assumptions. By using variational methods, we obtain the existence of solutions in the following case: if 2 0 such that for all λ ⩾ λ{sub 0}, we show that it has one nontrivial solution and there exist at least cat{sub Λ{sub δ}}(Λ) nontrivial solutions; if max(2,(4α)/(N−2α) ) 0.
Authors:
 [1] ;  [2] ;  [1] ;  [3]
  1. Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023 (China)
  2. (China)
  3. School of Science, Jiangnan University, Wuxi 214122 (China)
Publication Date:
OSTI Identifier:
22251777
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 12; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EQUATIONS; FUNCTIONS; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; POTENTIALS; VARIATIONAL METHODS