Eigenvalue criteria for existence of positive solutions Of second-order, multi-point, p-laplacian boundary value problems

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

In this paper we consider the existence and uniqueness of positive solutions of the multi-point boundary value problem (1) - (Øp(u?)?+(a+g(x,u,u?)Øp(u) =0, a.e. on (-1,1), (2) u(±1)=Si=1 ±ai±u(? i±) where p>1, Øp(s) p-2s, se R,m± = 1 are integer, and ?i±?(-1,1), ai± > 0, i=1 ,?,m±, Si=1ai± Also a ? L1(-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 languageEnglish
Pages (from-to)311-326
Number of pages16
JournalTopological Methods in Nonlinear Analysis
Volume36
Issue number2
Publication statusPublished - 2010

Keywords

  • Positive solutions of nonlinear boundary value problems
  • Principal eigenvalues

Fingerprint Dive into the research topics of 'Eigenvalue criteria for existence of positive solutions Of second-order, multi-point, p-laplacian boundary value problems'. Together they form a unique fingerprint.

  • Cite this