Existence, uniqueness and multiplicity of nontrivial solutions for biharmonic equations

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. For more information see https://ejde.math.txstate.edu/Volumes/2025/52/abstr.html