Electron. J. Differential Equations, Vol. 2018 (2018), No. 177, pp. 1-9.

Sufficient conditions for the existence of non-oscillatory solutions to first-order differential equations with multiple advanced arguments

Julio G. Dix

Abstract:
This article concerns the existence of non-oscillatory solutions to the equation
$$ x'(t)=\sum_{k=1}^m a_k(t) x(h_k(t)), $$
where $a_k\geq 0$ and $h_k(t)\geq t$. We generalize existing results and then give an answer to the open question stated in [4]. Moreover we present a new condition based on the integral of $(\sum a_k)^2$.

Submitted October 5, 2018. Published October 31, 2018.
Math Subject Classifications: 34K06, 34K11.
Key Words: Advanced linear differential equation; positive solution; oscillatory solution.

Show me the PDF file (219 KB), TEX file for this article.

Julio G. Dix
Department of Mathematics
Texas State University
601 University Drive
San Marcos, TX 78666, USA
email: jd01@txstate.edu

Return to the EJDE web page