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

Published online by Cambridge University Press:  14 November 2011

Gustavo Perla Menzala
Gustavo Perla Menzala
Affiliation:
Instituto de Mathematica, Universidade Federai do Rio de Janeiro, Caixa Postai 1835, ZC-00 20.000, Rio de Janeiro, RJ, Brasil
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Synopsis

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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 86 , Issue 3-4 , 1980 , pp. 291 - 301
Copyright
Copyright © Royal Society of Edinburgh 1980

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