### Abstract

In this paper we consider the existence and uniqueness of positive solutions of the multi-point boundary value problem (1) - (Ø_{p}(u?)?+(a+g(x,u,u?)Ø_{p}(u) =0, a.e. on (-1,1), (2) u(±1)=S_{i}=1 ^{±}a_{i}^{±}u(? _{i}^{±}) where p>1, Ø_{p}(s) ^{p-2}s, se R,m± = 1 are integer, and ?_{i}^{±}?(-1,1), a_{i}^{±} > 0, i=1 ,?,m^{±}, S_{i}=1^{m±}a_{i}^{±} Also a ? L^{1}(-1,1) and g: [-1,1]× R ^{2}?R is Carath´eodory, with (3) g(x,0,0)=0, x ?[-1,1]. Our criteria for existence of positive solutions of (1), (2) will be expressed in terms of the asymptotic behaviour of g(x, s, t), as s ? 8, and the principal eigenvalues of the multi-point boundary value problem consisting of the equation (4) -Ø(u?)?+aØp(u)= ?Øp(u), on (-1,1) Copyright © 2010 Juliusz Schauder Center for Nonlinear Studies.

Original language | English |
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Pages (from-to) | 311-326 |

Number of pages | 16 |

Journal | Topological Methods in Nonlinear Analysis |

Volume | 36 |

Issue number | 2 |

Publication status | Published - 2010 |

### Keywords

- Positive solutions of nonlinear boundary value problems
- Principal eigenvalues