Multiplicity results for nonhomogenous elliptic equation involving the generalized Paneitz-Branson operator

Kamel Tahri

Abstract


Let \((M,g)\) be a compact Riemannian manifold of dimension \(n\geq 3\), we consider the multiplicity results of solutions of the following nonhomogenous fourth order elliptic equation involving the generalized Paneitz-Branson operator:
\[ P_{g}(u)=f(x)|u|^{2^{♯}-2}u+h(x).\]
Under some conditions and using critical points theory, we prove the existence of two solutions of the elliptic equation. At the end, we give a geometric example when the equation has negative and positive solutions.

Keywords


Riemannian manifold, multiplicity result, nonhomogenous, Paneitz- Branson operator, critical points theory

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DOI: http://dx.doi.org/10.24193/subbmath.2023.4.19

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