Asymptotic Behavior of Solutions of the Third Order Nonlinear Mixed Type Neutral Differential Equations

The objective of our paper is to study asymptotic properties of the class of third order neutral differential equations with advanced and delayed arguments. Our results supplement and improve some known results obtained in the literature. An illustrative example is provided.

Positive solutions to Sturm–Liouville problems with non-local boundary conditions

In this paper, the existence of at least three non-negative solutions to non-local boundary-value problems for second-order differential equations with deviating arguments α and ϛ is investigated. Sufficient conditions, which guarantee the existence of positive solutions, are obtained using the Avery–Peterson theorem. We discuss our problem for both advanced and delayed arguments. An example is added to illustrate the results.