Positive solutions and eigenvalue intervals for nonlinear systems

Jifeng Chu; Donal O'Regan; Meirong Zhang

doi:10.1007/s12044-007-0007-z

Positive solutions and eigenvalue intervals for nonlinear systems

Jifeng Chu
, Donal O'Regan
, Meirong Zhang

Mathematics

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

7 Citations (Scopus)

Abstract

This paper deals with the existence of positive solutions for the nonlinear system (q(t)φ(p(t)u′₁(t)))′ + fⁱ(t, u) = 0, 0 < t < 1, i = 1, 2, . . . ,n. This system often arises in the study of positive radial solutions of nonlinear elliptic system. Here u = (u ₁, . . .,u_n) and fⁱ, i = 1, 2, . . ., n are continuous and nonnegative functions, p(t), q(t): [0, 1) → (0, ∞) are continuous functions. Moreover, we characterize the eigenvalue intervals for (q(t)φ(p(t)u′_i(t)))′ + λh_i(t)g ⁱ(u) = 0, 0 < t < 1, i = 1, 2,. . . ,n. The proof is based on a well-known fixed point theorem in cones.

Original language	English
Pages (from-to)	85-95
Number of pages	11
Journal	Proceedings of the Indian Academy of Sciences: Mathematical Sciences
Volume	117
Issue number	1
DOIs	https://doi.org/10.1007/s12044-007-0007-z
Publication status	Published - Feb 2007

Keywords

Eigenvalue intervals
Fixed point theorem in cones
Nonlinear system
p-Laplacian
Positive solutions

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10.1007/s12044-007-0007-z

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title = "Positive solutions and eigenvalue intervals for nonlinear systems",

abstract = "This paper deals with the existence of positive solutions for the nonlinear system (q(t)φ(p(t)u′1(t)))′ + fi(t, u) = 0, 0 < t < 1, i = 1, 2, . . . ,n. This system often arises in the study of positive radial solutions of nonlinear elliptic system. Here u = (u 1, . . .,un) and fi, i = 1, 2, . . ., n are continuous and nonnegative functions, p(t), q(t): [0, 1) → (0, ∞) are continuous functions. Moreover, we characterize the eigenvalue intervals for (q(t)φ(p(t)u′i(t)))′ + λhi(t)g i(u) = 0, 0 < t < 1, i = 1, 2,. . . ,n. The proof is based on a well-known fixed point theorem in cones.",

keywords = "Eigenvalue intervals, Fixed point theorem in cones, Nonlinear system, p-Laplacian, Positive solutions",

author = "Jifeng Chu and Donal O'Regan and Meirong Zhang",

year = "2007",

month = feb,

doi = "10.1007/s12044-007-0007-z",

language = "English",

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pages = "85--95",

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}

TY - JOUR

T1 - Positive solutions and eigenvalue intervals for nonlinear systems

AU - Chu, Jifeng

AU - O'Regan, Donal

AU - Zhang, Meirong

PY - 2007/2

Y1 - 2007/2

N2 - This paper deals with the existence of positive solutions for the nonlinear system (q(t)φ(p(t)u′1(t)))′ + fi(t, u) = 0, 0 < t < 1, i = 1, 2, . . . ,n. This system often arises in the study of positive radial solutions of nonlinear elliptic system. Here u = (u 1, . . .,un) and fi, i = 1, 2, . . ., n are continuous and nonnegative functions, p(t), q(t): [0, 1) → (0, ∞) are continuous functions. Moreover, we characterize the eigenvalue intervals for (q(t)φ(p(t)u′i(t)))′ + λhi(t)g i(u) = 0, 0 < t < 1, i = 1, 2,. . . ,n. The proof is based on a well-known fixed point theorem in cones.

AB - This paper deals with the existence of positive solutions for the nonlinear system (q(t)φ(p(t)u′1(t)))′ + fi(t, u) = 0, 0 < t < 1, i = 1, 2, . . . ,n. This system often arises in the study of positive radial solutions of nonlinear elliptic system. Here u = (u 1, . . .,un) and fi, i = 1, 2, . . ., n are continuous and nonnegative functions, p(t), q(t): [0, 1) → (0, ∞) are continuous functions. Moreover, we characterize the eigenvalue intervals for (q(t)φ(p(t)u′i(t)))′ + λhi(t)g i(u) = 0, 0 < t < 1, i = 1, 2,. . . ,n. The proof is based on a well-known fixed point theorem in cones.

KW - Eigenvalue intervals

KW - Fixed point theorem in cones

KW - Nonlinear system

KW - p-Laplacian

KW - Positive solutions

UR - https://www.scopus.com/pages/publications/34248181596

U2 - 10.1007/s12044-007-0007-z

DO - 10.1007/s12044-007-0007-z

M3 - Article

AN - SCOPUS:34248181596

SN - 0253-4142

VL - 117

SP - 85

EP - 95

JO - Proceedings of the Indian Academy of Sciences: Mathematical Sciences

JF - Proceedings of the Indian Academy of Sciences: Mathematical Sciences

IS - 1

ER -

Positive solutions and eigenvalue intervals for nonlinear systems

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