Bifurcation Results for the Mean Curvature Equations Defined on all ℝN

  • Stavrakakis, N. M.
  • Zographopoulos, N. B.

  • Department of Mathematics, National Technical University, Zografou Campus, 157 80 Athens, Greece

E-mail: [email protected]

[email protected]

Geometriae Dedicata 91(1):p 71-84, April 2002.

We prove certain local bifurcation results for the mean curvature problem. −∇ (∇u/√(1+|∇u|2)) = λf(x, u), x ∈ ℝN. This is achieved by applying standard local bifurcation theory. The use of certain equivalent weighted and homogeneous Sobolev spaces was proved to be crucial.

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