含超线性项的广义Choquard-Pekar方程基态解的存在性

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O175.25

Yu Chun, Wan Youyan. The Existence of Ground State to the Generalized Choquard-Pekar Equation with Superlinear Nonlinearities[J].Acta mathematica scientia,Series A, 2018, 38(2): 276-283.

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[1] Pekar S. Untersucheng über die Elektronentheorie der Kristalle. Berlin:Akademie Verlag, 1954
[2] Alexandrov A S, Devreese J T. Advances in Polaron Physics. Berlin:Springer, 2010
[3] Lieb E H. Existence and uniqueness of the minimizing solution of choquards nonlinear equation. Stud Appl Math, 1976/1977, 57:93-105
[4] Lions P L. Solutions of Hartree-Fock equations for colomb system. Comm Math Phys, 1987, 109:33-97
[5] Alves C, Yang M. Existence of semiclassical ground state solutions for a generalized Choquard equation. J Diff Eq, 2014, 257:4133-4164
[6] D'Avenia P, Siciliano G, Squassina M. On fractional Choquard equation. Math Models and Methods in Appl Sciences, 2015, 25:1447-1476
[7] Cingolani S, Clapp M, Secchi S. Multiple solutions to magnetic nonlinear Choquard equation. Z Angew Math Phys, 2012, 63:233-248
[8] Ma L, Zhao L. Classification of positive solitary solutions of the nonlinear Choquard equation. Arch Ration Mech Anal, 2010, 195:455-467
[9] Melgaard M, Zongo F. Multiple solutions of the quasirelativistic Choquard equation. J Math Phys, 2012, 53:033709
[10] Moroz V, Schaftingen Van. Semi-classical states for the Choquard equation. Calc Var Partial Differential Equations, 2015, 52:199-235
[11] Wei J, Winter M. Strongly interacting bumps for the Schrödinger-Newton equations. J Math Phys, 2009, 50:012905
[12] Zhang Z, Tassilo K, Hu A, Xia H. Existence of a nontrivial solution for Choquard's equation. Acta Mathematica Scientia, 2006, 26B(3):460-468
[13] Sun X, Zhang Y. Multi-peak solution for nonlinear magnetic Choquard type equation. J Math Phys, 2014, 55(3):1731-1769
[14] 曹道珉.广义Choquard-Pekar方程非平凡解的存在性. 数学物理学报,1989, 9A(1):101-112Cao D M. The existence of nontrivial solution to the generalized Choquard-Pekar equation. Acta Mathematica Scientia, 1989, 9A(1):101-112
[15] Stein E M, Weiss G. Fractional integrals in n-dimensional Euclidean spaces. J Math Mech, 1958, 7(4):503-514
[16] Chen W, Jin C, Li C, Lim J. Weighted Hardy-Littlewood-Sobolev inequalities and systems of integral equations. Discrete and Continuous Dynamical Systems, 2005, Supplement Volume:164-172
[17] Lions P L. The concentration-compactness principle in the calculus of variation. The locally compact case. Part I. Ann Inst H Poincaré Anal Non Linéaire, 1984, 1:109-145
[18] Lions P L. The concentration-compactness principle in the calculus of variation. The locally compact case. Part Ⅱ. Ann Inst H Poincaré Anal Non Linéaire, 1984, 1:223-283

The Existence of Ground State to the Generalized Choquard-Pekar Equation with Superlinear Nonlinearities

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