Existence of multiple positive solutions of inhomogeneous semilinear elliptic problems in unbounded domains

@article{Zhu1990ExistenceOM,
  title={Existence of multiple positive solutions of inhomogeneous semilinear elliptic problems in unbounded domains},
  author={Xiping Zhu and Huan-Song Zhou},
  journal={Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences},
  year={1990},
  volume={115},
  pages={301-318}
}
  • Xiping Zhu, Huan-Song Zhou
  • Published 1990
  • Mathematics
  • Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences
By using the concentration-compactness method of Lions [14, 16] and the mountain pass theorem of Ambrosetti and Rabinowitz [3], through a careful inspection of the energy balance for some sequence of approximated solutions, we show that under suitable conditions on f and h, the inhomogeneous problem. −Δu + c2u = λ(f(u) + h(x)) for x ∈ Ω (Ω is an exterior domain in ℝN, N≧ 3) and has at least two positive solutions. 
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