Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 39, Issue -, Pages 166-184Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2017.06.014
Keywords
Schrodinger-Poisson system; Critical nonlinearity; Sign-changing solution; Ground state
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Funding
- National Natural Science Foundation of China [11471267]
- Chongqing Research Program of Basic Research and Frontier Technology [cstc2017jcyjAX0331]
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In this paper, we investigate the existence of ground state sign-changing solutions to a class of Schrodinger-Poisson systems {-Delta u + u + k(x)phi u = lambda f(x)u + vertical bar u vertical bar(4)u, x is an element of R-3, -Delta phi = k(x)u(2), x is an element of R-3, where k and f are nonnegative functions, 0 < lambda < lambda(1) and lambda(1) is the first eigenvalue of the problem -Delta u + u = lambda f(x)u in H-1 (R-3). With the help of the constraint variational method, we obtain that the Schrodinger-Poisson system possesses at least one ground state sign-changing solution for each 0 < lambda < lambda(l). Moreover, we prove that its energy is strictly larger than twice that of ground state solutions. This paper can be regarded as the complementary work of Huang et al. (2013), Shuai and Wang (2015), Wang and Zhou (2015) and Zhang (2015). (C) 2017 Elsevier Ltd. All rights reserved.
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