Existence of Solutions for a Class of \(p\)-biharmonic Equations with Navier Boundary Conditions

The p-biharmonic equation with Navier boundary conditions is an important class of higher-order nonlinear elliptic equations that arises in applications such as beam vibration theory and suspension bridge dynamics. Extensive research has employed variational methods and critical point theory to establish the existence and multiplicity of solutions, highlighting its significance in both mathematical analysis and engineering applications. This paper studies the existence of solutions for a class of p-biharmonic equations with Navier boundary conditions. Using Morse theory, critical point theory and the G-link theorem, we establish the existence and multiplicity of solutions under the nonquadratic type conditions and the asymptotic noncrossing condition.