### Abstract

We prove that appropriate combinations of superlinearity and sublinearity of f(u) with respect to Φ at zero and infinity guarantee the existence, multiplicity, and nonexistence of positive solutions to boundary value problems for the n-dimensional system (Φ(u′) ′ + λh(t)f(u) = 0, 0 < t < 1. The vector-valued function Φ is defined by Φ(u′) = ( (u_{1}′ ,..., (u_{n}′)), where u = (u_{1},...,u_{n} and covers the two important cases (u′) = u′ and (u′) = u′ ^{p-2}u′, p > 1. Our methods employ fixed point theorems in a cone.

Original language | English (US) |
---|---|

Pages (from-to) | 287-306 |

Number of pages | 20 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 281 |

Issue number | 1 |

State | Published - May 1 2003 |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Journal of Mathematical Analysis and Applications*,

*281*(1), 287-306.

**On the number of positive solutions of nonlinear systems.** / Wang, Haiyan.

Research output: Contribution to journal › Article

*Journal of Mathematical Analysis and Applications*, vol. 281, no. 1, pp. 287-306.

}

TY - JOUR

T1 - On the number of positive solutions of nonlinear systems

AU - Wang, Haiyan

PY - 2003/5/1

Y1 - 2003/5/1

N2 - We prove that appropriate combinations of superlinearity and sublinearity of f(u) with respect to Φ at zero and infinity guarantee the existence, multiplicity, and nonexistence of positive solutions to boundary value problems for the n-dimensional system (Φ(u′) ′ + λh(t)f(u) = 0, 0 < t < 1. The vector-valued function Φ is defined by Φ(u′) = ( (u1′ ,..., (un′)), where u = (u1,...,un and covers the two important cases (u′) = u′ and (u′) = u′ p-2u′, p > 1. Our methods employ fixed point theorems in a cone.

AB - We prove that appropriate combinations of superlinearity and sublinearity of f(u) with respect to Φ at zero and infinity guarantee the existence, multiplicity, and nonexistence of positive solutions to boundary value problems for the n-dimensional system (Φ(u′) ′ + λh(t)f(u) = 0, 0 < t < 1. The vector-valued function Φ is defined by Φ(u′) = ( (u1′ ,..., (un′)), where u = (u1,...,un and covers the two important cases (u′) = u′ and (u′) = u′ p-2u′, p > 1. Our methods employ fixed point theorems in a cone.

UR - http://www.scopus.com/inward/record.url?scp=0038346720&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038346720&partnerID=8YFLogxK

M3 - Article

VL - 281

SP - 287

EP - 306

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -