Three positive solutions for m-point boundary-value problems with one-dimensional p-Laplacian

In this article, we study the multipoint boundary value problem for the one-dimensional p-Laplacian $$ (phi_p(u'))'+ q(t)f(t,u(t),u'(t))=0,quad tin (0,1), $$ subject to the boundary conditions $$ u(0)=sum_{i=1}^{m-2} a_iu(xi_i),quad u'(1)=eta u'(0). $$ Using a fixed point th...

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Bibliographic Details
Published inElectronic journal of differential equations Vol. 2011; no. 75; pp. 1 - 10
Main Authors Donglong Bai, Hanying Feng
Format Journal Article
LanguageEnglish
Published Texas State University 16.06.2011
Subjects
Avery-Peterson fixed point theorem
Multipoint boundary value problem
one-dimensional p-Laplacian
positive solution
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Summary:In this article, we study the multipoint boundary value problem for the one-dimensional p-Laplacian $$ (phi_p(u'))'+ q(t)f(t,u(t),u'(t))=0,quad tin (0,1), $$ subject to the boundary conditions $$ u(0)=sum_{i=1}^{m-2} a_iu(xi_i),quad u'(1)=eta u'(0). $$ Using a fixed point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The interesting point is that the nonlinear term f involves the first derivative of the unknown function.
ISSN:1072-6691