Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (5): 1347-1356.
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Received:
2021-01-18
Online:
2021-10-26
Published:
2021-10-08
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Peng Chen. Ground State Solutions of Nehari-Pohozaev Type for a Class of Reaction-Diffusion System[J].Acta mathematica scientia,Series A, 2021, 41(5): 1347-1356.
1 |
Bartsch T , Ding Y . Homoclinic solutions of an infinite-dimensional Hamiltonian system. Math Z, 2002, 240, 289- 310
doi: 10.1007/s002090100383 |
2 | Clment P , Felmer P , Mitidieri E . Homoclinic orbits for a class of infinite dimensional Hamiltonian systems. Ann Sc Norm Super Pisa, 1997, 24, 367- 393 |
3 |
De Figueiredo D , Ding Y . Strongly indefinite functions and multiple solutions of elliptic systems. Trans Amer Math Soc, 2003, 355, 2973- 2989
doi: 10.1090/S0002-9947-03-03257-4 |
4 | De Figueiredo D , Felmer P L . On superquadiatic elliptic systems. Trans Amer Math Soc, 1994, 343, 97- 116 |
5 |
Ding Y , Luan S , Willem M . Solutions of a system of diffusion equations. J Fixed Point Theory Appl, 2007, 2, 117- 139
doi: 10.1007/s11784-007-0023-8 |
6 | Ding Y . Variational Methods for Strongly Indefinite Problems. Singapore: World Scientific Press, 2008 |
7 | Ding Y , Xu T . Effect of external potentials in a coupled system of multi-component incongruent diffusion. Topol Method Nonl Anal, 2019, 54, 715- 750 |
8 | Ding Y , Xu T . Concentrating patterns of reaction-diffusion systems: a variational approach. Trans Amer Math Soc, 2007, 369, 97- 138 |
9 | Gu L , Zhou H . An improved fountain Theorem and its application. Adv Nonlinear Stud, 2016, 17 (4): 727- 738 |
10 |
Guo Y , Zeng X , Zhou H . Energy estimates and symmetry breaking in attractive Bose-Einstein condensates with ring-shaped potentials. Ann I H Poincare-AN, 2016, 33 (3): 809- 828
doi: 10.1016/j.anihpc.2015.01.005 |
11 | Itô S . Diffusion Equations. Providence, RI: American Mathematical Society, 1992 |
12 | Vazquez J L. The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion//Bonforte M, Grillo G. Nonlocal and Nonlinear Diffusions and Interactions: New Methods and Directions. Berlin: Springer, 2017: 205-278 |
13 | Kryszewski W , Szulkin A . An infinite dimensional morse theorem with applications. Trans Amer Math Soc, 1997, 349, 3184- 3234 |
14 |
Li G , Szulkin A . An asymptotically periodic Schrödinger equation with indefinite linear part. Commun Contemp Math, 2002, 4, 763- 776
doi: 10.1142/S0219199702000853 |
15 |
Li G , Yang J . Asymptotically linear elliptic systems. Comm Partial Differential Equations, 2004, 29, 925- 954
doi: 10.1081/PDE-120037337 |
16 | Nagasawa M . Schrödinger Equations and Diffusion Theory. Boston: Birkhäuser, 1993 |
17 |
Saad M , Gomez J . Analysis of reaction-diffusion system via a new fractional derivative with non-singular kernel. Physica A, 2018, 509, 703- 716
doi: 10.1016/j.physa.2018.05.137 |
18 |
Szulkin A , Weth T . Ground state solutions for some indefinite problems. J Funct Anal, 2009, 257, 3802- 3822
doi: 10.1016/j.jfa.2009.09.013 |
19 |
Tang X , Chen S , Lin X , Yu J . Ground state solutions of Nehari-Pankov type for Schrödinger equations with local super-quadratic conditions. J Differ Equa, 2020, 268, 4663- 4690
doi: 10.1016/j.jde.2019.10.041 |
20 | Tang X . Non-Nehari manifold method for superlinear Schrödinger equation. Taiwanese J Math, 2014, 18, 1957- 1979 |
21 | Tang X, Chen S. Ground state solutions of Nehari-Pohozaev type for Kirchhoff-type problems with general potentials. Calc Var Partial Differential Equations, 2017, 55, Article nomber: 110 |
22 | Wang Z , Zhou H . Radial sign-changing solution for fractional Schrodinger equation. Discrete Cont Dyn-A, 2016, 36 (1): 499- 508 |
23 |
Wei Y , Yang M . Existence of solutions for a system of diffusion equations with spectrum point zero. Z Angew Math Phys, 2014, 65, 325- 337
doi: 10.1007/s00033-013-0334-0 |
24 |
Yang M , Shen Z , Ding Y . On a class of infinite-dimensional Hamiltonian systems with asymptotically periodic nonlinearities. Chinese Ann Math, 2011, 32B (1): 45- 58
doi: 10.1007/s11401-010-0625-0 |
25 |
Yang M . Nonstationary homoclinic orbits for an infinite-dimensional Hamiltonian system. J Math Phys, 2010, 51, 102701
doi: 10.1063/1.3488967 |
26 |
Zeng X , Zhang Y , Zhou H . Positive solutions for a quasilinear Schrödinger equation involving Hardy potential and critical exponent. Commun Contemp Math, 2014, 16 (6): 1450034
doi: 10.1142/S0219199714500345 |
27 |
Zhang J , Tang X , Zhang W . Ground state solutions for superquadratic Hamiltonian elliptic systems with gradient terms. Nonlinear Anal, 2014, 95, 1- 10
doi: 10.1016/j.na.2013.07.027 |
28 |
Zhao F , Ding Y . On a diffusion system with bounded potential. Discrete Contin Dyn Syst, 2009, 23, 1073- 1086
doi: 10.3934/dcds.2009.23.1073 |
29 |
Zhao L , Zhao F . On ground state solutions for superlinear Hamiltonian elliptic systems. Z Angew Math Phys, 2013, 64, 403- 418
doi: 10.1007/s00033-012-0258-0 |
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