Academic Editor: Youssef EL FOUTAYENI
        
         
          | Received | Accepted | Published | 
         
          | January  28, 2021 | February 15, 2021 | March 15, 2021 | 
      
    
    
    Abstract:  In this work, we investigate the existence of nodal solutions for a fourth elliptic problem on smooth compact Riemannian manifold with boundary. The existence results assured by variational method under some geometric conditions.