Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 52, pp. 1-16.

Title: Existence and nonexistence of positive solutions for fourth-order elliptic problems
       
Authors: Meiqiang Feng (Beijing Information Science and Tech. Univ., Beijing, China)
         Haiping Chen (Beijing Information Science and Tech. Univ., Beijing, China)
         
Abstract: 
This article studies a fourth-order elliptic problem with and without an 
eigenvalue parameter. New criteria for the existence and nonexistence of 
positive solution are established under some sublinear conditions which 
involve the principal eigenvalues of the corresponding linear problems. 
The interesting point is that the nonlinear term $f$ is involved in the 
second-order derivative explicitly.

Submitted June 27, 2023. Published August 06, 2023.
Math Subject Classifications: 35J60, 35J40.
Key Words: Fourth-order elliptic problems; Navier boundary conditions;
    positive solution; existence, uniqueness and nonexistence; principle eigenvalue.