Dynamics of Partial Differential Equations

Volume 6 (2009)

Number 3

Existence and multiplicity of solutions to elliptic equations of fourth order on compact manifolds

Pages: 203 – 225

DOI: https://dx.doi.org/10.4310/DPDE.2009.v6.n3.a1

Author

Mohammed Benalili (Department of Mathematics, University Abou-Bekr Belkaïd, Tlemcen, Algeria)

Abstract

This paper deals with a fourth order elliptic equation on compact Riemannian manifolds, the function ƒ involved in the nonlinearity is of changing sign which makes the analysis more difficult than the case where ƒ is of constant sign.We prove the multiplicity of solutions in the subcritical case which is the subject of the first theorem. In the second one we establish the existence of solutions to the equation with critical Sobolev growth.

Keywords

elliptic equation of fourth order, critical Sobolev exponent

2010 Mathematics Subject Classification

58J05

Published 1 January 2009