Lyapunov-type inequalities for odd order linear differential equations

Abstract

In this article, we obtain Lyapunov-type inequalities for certain odd order linear boundary-value problems. Our inequalities involve integrals of both $q_+(t)$ and $q_-(t)$ in addition to that of $|q(t)|$. The Green's function for even order boundary-value problems plays a key role in our proofs. Also, using the Fredholm alternative theorem, we obtain a criterion for the existence and uniqueness of solutions to the corresponding nonhomogeneous linear boundary-value problems.

Keywords

• Lyapunov-type inequalities
• odd order
• linear differential equations
• Green's function
• boundary value problem