Sougata Dhar, Qingkai Kong
Abstract:
In this article, we obtain Lyapunov-type inequalities for certain
odd order linear boundary-value problems. Our inequalities involve
integrals of both
and
in addition to that of
.
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.
Submitted July 7, 2015. Published September 7, 2016.
Math Subject Classifications: 34A40, 34B05, 34C11, 26D20.
Key Words: Lyapunov-type inequalities; odd order; linear differential equations;
Green's function; boundary value problem.
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Sougata Dhar Department of Mathematics Northern Illinois University DeKalb, IL 60115, USA email: sdhar@niu.edu | |
Qingkai Kong Department of Mathematics Northern Illinois University DeKalb, IL 60115, USA email: qkong@niu.edu |
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