Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 52, pp. 1-16.

Title: Existence, uniqueness and multiplicity of nontrivial solutions for biharmonic equations

Authors: Meiqiang Feng (Beijing Information Science and Tech. Univ., China)
         Yichen Lu (Beijing Information Science and Tech. Univ., China)

Abstract:
We study the existence of nontrivial weak solutions for biharmonic equations 
with Navier and with Dirichlet boundary conditions.
This is done by using critical point theory for even functionals, and
the theory of strongly monotone operators. 
Also we analyze the existence of infinitely many weak solutions.
This is probably the first time that the theory of strongly monotone 
operator is used to study biharmonic equations.

Submitted February 4, 2025. Published May 24, 2025.
Math Subject Classifications: 35J35, 35J40.
Key Words: Biharmonic equation; Caratheodory conditions;  monotone mapping; 
 mountain pass lemma; existence, uniqueness and multiplicity.