Nehari manifold approach to singular fourth-order Leray–Lions equations with no-flux boundary conditions

Abstract

Purpose In this paper, we study a fourth-order singular problems of type Leray–Lions with singular weight and with no-flux boundary conditions. Design/methodology/approach We use the Nehari manifold to establish our result for our problem. Findings We prove that there exist at least two nontrivial positive weak solutions. Originality/value In particular, it investigates the problem in the presence of singular weights and variable exponents, a case that has not been extensively studied in the existing literature.