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  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 134, Issue 1
  • February 2004, pp. 191-200

Existence of a positive solution of an elliptic equation on RN

  • Zhaoli Liu (a1) and Zhi-Qiang Wang (a2)
  • DOI: http://dx.doi.org/10.1017/S0308210500003152
  • Published online: 12 July 2007
Abstract

We prove the existence of a positive solution for the Schrödinger-type equation on RN,−Δu + V(x)u = f(u) for uH1(RN), provided that The result is obtained in two cases. (a) lim|x|→ ∞V(x) = V (∞) ∈ (0,∞), f is subcritical and supt>0 2F(t)t−2 < V (∞). (b) There exist V > 0 and R* > 0 such that f(t)t−1 < V ∞ ≤ V (x) for all t > 0 and |x| ≥ R*.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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