期刊
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
卷 12, 期 6, 页码 1069-1092出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219199710004068
关键词
Infinitely many solutions; non-radial solutions; reduction argument; Schrodinger-Poisson system
资金
- NSFC [10631030]
- Program for New Century Excellent Talents in University [07-0350]
- MOE [CCNU09C01007]
- ARC in Australia
We consider the following nonlinear Schrodinger-Poisson system in R-3 {-Delta u + u + K(vertical bar y vertical bar)Phi(y)u = Q(vertical bar y vertical bar)vertical bar u vertical bar(p-1)u, y is an element of R-3, -Delta Phi= K(vertical bar y vertical bar)u(2), y is an element of R-3, (0.1) where K(r) and Q(r) are bounded and positive functions, 1 < p < 5. Assume that K(r) and Q(r) have the following expansions (as r -> +infinity): K(r) = a/r(m) + O (1/r(m+theta)), Q(r) = Q(0) + b/r(n) + O(1/r(n+kappa)), where a > 0, b is an element of R, m > 1/2, n > 1, theta > 0, kappa > 0, and Q(0) > 0 are some constants. We prove that (0.1) has infinitely many non-radial positive solutions if b < 0, or if b >= 0 and 2m < n.
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