CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

Existence and Multiplicity of Positive Solutions for Singular Semipositone $p$-Laplacian Equations

  Published:2006-06-01
 Printed: Jun 2006
  • Ravi P. Agarwal
  • Daomin Cao
  • Haishen Lü
  • Donal O'Regan
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

Positive solutions are obtained for the boundary value problem \[\begin{cases} -( | u'| ^{p-2}u')' =\lambda f( t,u),\;t\in ( 0,1) ,p>1\\ u( 0) =u(1) =0. \end{cases} \] Here $f(t,u) \geq -M,$ ($M$ is a positive constant) for $(t,u) \in [0\mathinner{,}1] \times (0,\infty )$. We will show the existence of two positive solutions by using degree theory together with the upper-lower solution method.
Keywords: one dimensional $p$-Laplacian, positive solution, degree theory, upper and lower solution one dimensional $p$-Laplacian, positive solution, degree theory, upper and lower solution
MSC Classifications: 34B15 show english descriptions Nonlinear boundary value problems 34B15 - Nonlinear boundary value problems
 

© Canadian Mathematical Society, 2014 : http://www.cms.math.ca/