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

R. P. Agarwal; Haishen Lü; D. O'Regan

doi:10.4171/ZAA/1168

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

R. P. Agarwal
, Haishen Lü
, D. O'Regan

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

4 Citations (Scopus)

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 C¹[0,1] positive solutions and a sufficient condition for the existence of C[0,1] positive solutions are presented.

Original language	English
Pages (from-to)	689-709
Number of pages	21
Journal	Zeitschrift für Analysis und ihre Anwendungen
Volume	22
Issue number	3
DOIs	https://doi.org/10.4171/ZAA/1168
Publication status	Published - 2003

Keywords

Existence conditions for solutions
Positive solutions
Singular boundary value problems

Access to Document

10.4171/ZAA/1168

Cite this

@article{4f9cbf7d9eb04b12b10990a533559955,

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

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 C1[0,1] positive solutions and a sufficient condition for the existence of C[0,1] positive solutions are presented.",

keywords = "Existence conditions for solutions, Positive solutions, Singular boundary value problems",

author = "Agarwal, \{R. P.\} and Haishen L{\"u} and D. O'Regan",

year = "2003",

doi = "10.4171/ZAA/1168",

language = "English",

volume = "22",

pages = "689--709",

journal = "Zeitschrift f{\"u}r Analysis und ihre Anwendungen",

issn = "0232-2064",

publisher = "European Mathematical Society Publishing House",

number = "3",

}

TY - JOUR

T1 - A Necessary and Sufficient Condition for the Existence of Positive Solutions to the Singular p-Laplacian

AU - Agarwal, R. P.

AU - Lü, Haishen

AU - O'Regan, D.

PY - 2003

Y1 - 2003

N2 - 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 C1[0,1] positive solutions and a sufficient condition for the existence of C[0,1] positive solutions are presented.

AB - 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 C1[0,1] positive solutions and a sufficient condition for the existence of C[0,1] positive solutions are presented.

KW - Existence conditions for solutions

KW - Positive solutions

KW - Singular boundary value problems

UR - https://www.scopus.com/pages/publications/0344549780

U2 - 10.4171/ZAA/1168

DO - 10.4171/ZAA/1168

M3 - Article

SN - 0232-2064

VL - 22

SP - 689

EP - 709

JO - Zeitschrift für Analysis und ihre Anwendungen

JF - Zeitschrift für Analysis und ihre Anwendungen

IS - 3

ER -

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this