Existence and uniqueness for a semilinear sixth-order ODE

Abstract

By using variational methods and maximum principles we discuss the existence, uniqueness and multiplicity of solutions for a semilinear sixth-order ODE. The main difference between our work and other related papers is that we treat a general case and we do not impose sign restrictions on the nonlinearity $f$ or on its potential $F$.

Keywords

• ode
• sixth-order
• semilinear
• variational method