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

Ravi P. Agarwal; Haishen Lü; Donal O'Regan

doi:10.4171/zaa/1168

JournalszaaVol. 22, No. 3pp. 689–709

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

Ravi P. Agarwal
Texas A&M University, Kingsville, United States
Haishen Lü
The Chinese Academy of Sciences, Beijing, China
Donal O'Regan
National University of Ireland, Galway, Ireland

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Abstract

This paper studies the boundary value problem

(φ_{p} (u^{'}))^{'} + q (t) (f (u) + g (u)) = 0 (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.

Cite this article

Ravi P. Agarwal, Haishen Lü, Donal O'Regan, A Necessary and Sufficient Condition for the Existence of Positive Solutions to the Singular p-Laplacian. Z. Anal. Anwend. 22 (2003), no. 3, pp. 689–709

DOI 10.4171/ZAA/1168