Existence and nonexistence of positive solutions for fourth-order elliptic problems

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. For more information see https://ejde.math.txstate.edu/Volumes/2023/52/abstr.html