The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (257 KB) | Abstract as PDF | Metadata | Table of Contents | ZAA summary
Volume 22, Issue 3, 2003, pp. 689–709
DOI: 10.4171/ZAA/1168

Published online: 2003-09-30

A Necessary and Sufficient Condition for the Existence of Positive Solutions to the Singular p-Laplacian

Ravi P. Agarwal[1], Haishen Lü[2] and Donal O'Regan[3]

(1) Texas A&M University, Kingsville, United States
(2) The Chinese Academy of Sciences, Beijing, China
(3) National University of Ireland, Galway, Ireland

This paper studies the boundary value problem $$ (\varphi_p(u'))' + q(t)(f(u) + g(u)) = 0 \qquad (0 < t < 1) $$ $$ \ \ u(0) = u(1) = 0 $$ in the case $p > 1$. A necessary and sufficient condition for the existence of $C^1[0,1]$ positive solutions and a sufficient condition for the existence of $C[0,1]$ positive solutions are presented.

Keywords: Singular boundary value problems, positive solutions, existence conditions for solutions

Agarwal Ravi, Lü Haishen, O'Regan Donal: A Necessary and Sufficient Condition for the Existence of Positive Solutions to the Singular p-Laplacian. Z. Anal. Anwend. 22 (2003), 689-709. doi: 10.4171/ZAA/1168