具外部位势分数阶Choquard方程的基态解Ground states for fractional Choquard equations with external potential
刘瑞娜;章国庆;刘三阳;
摘要(Abstract):
研究具外部位势非自治分数阶Choquard方程:{(-?)su+mu+V(x)u=(1+a(x))(I_α*|u|p)|u|su+mu+V(x)u=(1+a(x))(I_α*|u|p)|u|(p-2)u,x∈R(p-2)u,x∈RN u(x)→0,当|x|→∞时,基态解的存在性.利用Nehari流形技巧、集中紧性原理和山路引理得到了基态解的存在性.
关键词(KeyWords): 分数阶Choquard方程;外部位势;基态解
基金项目(Foundation): 国家自然科学基金(11771291)
作者(Authors): 刘瑞娜;章国庆;刘三阳;
参考文献(References):
- [1]Moroz V,Van Schaftingen J.Semi-classical states for the Choquard equation[J].Calculus of Variations and Partial Differential Equations,2015,52(1/2):199-235.
- [2]Secchi S.A note on Schrodinger–Newton systems with decaying electric potential[J].Nonlinear Analysis:Theory,Methods Applications,2010,72(9):3842-3856.
- [3]Clapp M,Salazar D.Positive and sign changing solutions to a nonlinear Choquard equation[J].Journal of Mathematical Analysis and Applications,2013,407(1):1-15.
- [4]Cingolani S,Secchi S.Ground states for the pseudo-relativistic Hartree equation with external potential[J].Proceedings of the Royal Society of Edinburgh:Section A Mathematics,2015,145(1):73-90.
- [5]Chen Y H,Liu C G.Ground state solutions for non-autonomous fractional Choquard equations[J].Nonlinearity,2016,29(6):1827.
- [6]Caffarelli L,Silvestre L.An extension problem related to the fractional Laplacian[J].Communications in Partial Differential Equations,2007,32(8):1245-1260.
- [7]Nezza E Di,Palatucci G,Valdinoci E.Hitchhiker's guide to the fractional Sobolev spaces[J].Bulletin des Sciences Mathematiques,2012,136(5):521-573.
- [8]Zelati V C,Nolasco M.Existence of ground states for nonlinear,pseudo-relativistic Schrodinger equations[J].Atti della accademia nazionale dei lincei,Rendiconti lincei,Matematica e applicazion,2011,22(1):51-72.
- [9]Lieb E H,Loss M.Analysis,Graduate Studies in Mathematics[M].2nd ed.USA:American Mathematical Society,2001.