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Existence of multiple positive solutions to nonhomogeneous Schrödinger–Poisson system

Author

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  • Zhang, Qi
  • Li, Fuyi
  • Liang, Zhanping

Abstract

In this paper, we consider the existence of multiple solutions to the following nonhomogeneous generalized Schrödinger–Poisson system-Δu+Ku+qϕf(u)=g(u)+h(x),inR3,-Δϕ=2qF(u),inR3,whereq⩾0is a parameter, 0≠h(x)=h(|x|)∈L2(R3), and g is asymptotically linear or superliner at infinity. We show that there exists q0>0 such that the system has at least two positive radial solutions for q∈[0,q0).

Suggested Citation

  • Zhang, Qi & Li, Fuyi & Liang, Zhanping, 2015. "Existence of multiple positive solutions to nonhomogeneous Schrödinger–Poisson system," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 353-363.
    • Handle: RePEc:eee:apmaco:v:259:y:2015:i:c:p:353-363
    DOI: 10.1016/j.amc.2015.02.044
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