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Multiple Solutions for a Class of Neumann Elliptic Problems on Compact Riemannian Manifolds with Boundary

  Published:2010-07-26
 Printed: Dec 2010
  • Alexandru Kristály,
    Babeş-Bolyai University, Department of Economics, 400591 Cluj-Napoca, Romania
  • Nikolaos S. Papageorgiou,
    National Technical University, Department of Mathematics, Zografou Campus, Athens, 15780, Greece
  • Csaba Varga,
    Babeş-Bolyai University, Faculty of Mathematics and Computer Science, 400084 Cluj-Napoca, Romania
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Abstract

We study a semilinear elliptic problem on a compact Riemannian manifold with boundary, subject to an inhomogeneous Neumann boundary condition. Under various hypotheses on the nonlinear terms, depending on their behaviour in the origin and infinity, we prove multiplicity of solutions by using variational arguments.
Keywords: Riemannian manifold with boundary, Neumann problem, sublinearity at infinity, multiple solutions Riemannian manifold with boundary, Neumann problem, sublinearity at infinity, multiple solutions
MSC Classifications: 58J05, 35P30 show english descriptions Elliptic equations on manifolds, general theory [See also 35-XX]
Nonlinear eigenvalue problems, nonlinear spectral theory
58J05 - Elliptic equations on manifolds, general theory [See also 35-XX]
35P30 - Nonlinear eigenvalue problems, nonlinear spectral theory
 

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