INFINITELY MANY POSITIVE SOLUTIONS FOR THE NONLINEAR SCHRÖDINGER–POISSON SYSTEM
2010 ◽
Vol 12
(06)
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pp. 1069-1092
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We consider the following nonlinear Schrödinger–Poisson system in ℝ3[Formula: see text] 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 → +∞): [Formula: see text] where a > 0, b ∈ ℝ, m > 1/2, n > 1, θ > 0, κ > 0, and Q0 > 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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