Skip to main content Accessibility help

On regular solutions of a nonlinear equation of Choquard's type

  • Gustavo Perla Menzala (a1)


We study the nonlinear equation

in ℝ3, where Δ denotes the Laplacian operator, and R and K are real-valued functions satisfying suitable conditions. We use a variational formulation to show the existence of a non-trivial weak solution of the above equation for some real number λ. Because of our assumptions on R and K we shall look for solutions which are spherically symmetric, decrease with r = |x| and vanish at infinity.



Hide All
1Bader, P.. Variational method for the Hartree equation of the helium atom. Proc. Roy. Soc. Edinburgh Sect. A 82 (1978), 2739.
2Brezis, H.. Nonlinear problems related to the Thomas-Fermi equation. North-Holland Math. Studies 30 (ed. de la Penha, G. and Medeiros, L. A.) (Amsterdam: North-Holland, 1977).
3Friedrichs, K.. Differentiability of solutions of elliptic partial differential equations. Comm. Pure Appl. Math. 5 (1953), 299326.
4Gustafson, K. and Sather, D.. A branching analysis of the Hartree equation. Rend. Mat. 4 (1971), 723734.
5Hardy, G. H., Littlewood, J. and Polya, G.. Inequalities (Cambridge Univ. Press, 1952).
6Hartree, D. R.. The calculations of atomic structures (New York: Wiley, 1957).
7Kato, T.. Perturbation theory for linear operators (New York: Springer-Verlag, 1966).
8Lieb, E. and Simon, B.. The Hartree-Fock theory for Coulomb systems. Comm. Math. Phys. 53 (1977), 185194.
9Lieb, E.. Existence and uniqueness of the minimizing solution of Choquard's nonlinear equation. Studies in Appi Math. 57 (1977), 93195.
10Reeken, M.. General theorem on bifurcation and its application to the Hartree equation of the Helium atom. J. Mathematical Phys. 11 (1970), 25052512.
11Strauss, W.. Existence of solitary waves in higher dimensions. Comm. Math. Phys. 55 (1977), 149162.
12Stuart, C. A.. Existence theory for the Hartree equation. Arch. Rational Mech. Anal. 51 (1973) 6069.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

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
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed