The existence and concentration of positive solutions for a nonlinear Schrödinger-Poisson system with critical growth

Journal Article · Sat Mar 15 00:00:00 EDT 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4868617· OSTI ID:22251033

Zhang, Jianjun ^[1]

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1. Chern Institute of Mathematics, Nankai University, Tianjin 300071 (China)

We consider the Schrödinger-Poisson system: −ε{sup 2}Δu + V(x)u + ϕ(x)u = f(u),−Δϕ = u{sup 2} in R{sup 3}, where the nonlinear term f is of critical growth. In this paper, we construct a solution (u{sub ε}, ϕ{sub ε}) of the above elliptic system, which concentrates at an isolated component of positive locally minimum points of V as ε → 0 under certain conditions on f. In particular, the monotonicity of (f(s))/(s{sup 3}) and the so-called Ambrosetti-Rabinowitz condition are not required.

• OSTI ID: 22251033
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

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GENERAL PHYSICS
CONCENTRATION RATIO
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS